What design decisions must I make to select a suitable P-Channel MOSFET
I need a PFET with a logic level gate to trigger a power connection to a hobby servo that pulls more current than my MCU pin can handle.  ... 
  I'm trying to understand how to go about designing the circuit so I can then choose from available devices that meet my need and can eliminate those that don't.


This is a purposefully excessively detailed response to the query.
It's intended as a tutorial of sorts in component selection generally and in small MOSFET selection specifically. This is not an especially demanding application and in some other cases much more detail may be required.

The aims include showing what may be involved in a typical relatively simple component selection process, what sort of not so obvious factors may hide in the background and how by selective refinement a bewilderingly large number of available devices may be reduced to a more manageable and more appropriate small subset. 

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Set the target:

From the available thousands of MOSFETs available, a subset that meet the design specification can be chosen by working out what the design specification is. This need not be done in infinitely find detail. Just "roughing out" the acceptable values for a number of parameters rapidly reduces the options to (more) manageable levels. Below I'll use relatively standard abbreviations with either approximate meanings given or none at all as they can be rapidly understood on inspection of the data sheets or selection tables or literature.  

Vdsmax - constrained by operating voltage.  

The MOSFET needs to operate on 5V, so a 10V or greater Vds rating is potentially OK. But a Vds of 20V or more is common, and more 'headroom' gives more robustness and resistance to 'the little things that go wrong' such as inductive spikes, so start by setting Vds >= 20V. This and other parameters can be loosened if the available range proves too low. 

Idsmax - maximum continuous operating current.  

The MOSFET must handle maximum servo current easily. You do not say what that is so it is assumed that 1A will be very adequate. If this is not the case a different value can be selected. The MOSFET needs an IDsmax rating of 1A but higher is common and usually useful. Higher Idsmax than required in operation usually results in devices with lower on resistance so lower losses at the desired operating current.

Rdson - Resistance when "fully enhanced".    

The voltage drop when turned on needs to be small enough to keep thermal losses in the MOSFET to an acceptable level. Acceptable may be based on temperature control of MOSFET, not too much loss in available voltage for the load and energy budget aspects). In this case a "fully turned on" resistance of 0.1 Ohm or less is probably OK and higher may well be acceptable. At 1A a Rdson of 0.1 Ohm drops 0.1V, dissipates 100 mW or 2% of a 5V supply. At 2A and Rdson of 0.2 Ohm drops 0.4V and dissipates 800 milliwatts or 4% of a 5V supply. The former (0.1 Ohm, 1A) is almost certainly acceptable in most cases and certainly for a servo and can be handled by a SOT23 SMD transistor with sensible PCB copper. The latter (0.2 Ohm, 2A) is thermally annoying for most SOT23 uses but would usually be OK with an eg DPak pkg, the voltage drop may be unacceptable in some cases and energy loss% is probably usually acceptable. so Rdson &lt;= 100 milliOhms will be acceptable at 1A and in many cases a modern PFET will give lower Rdson levels.  

Rdson - typical and real world values.
It is important to note that MOSFET Rdson values are usually (but not always) specified for stupidly short pulse values at unusually low duty cycles. This means the junction temperature is dominated mostly by thermal of the die and will remain near ambient temperature during the short pulse and have ample time to cool before the next pulse. In most real world situations much longer on times and higher duty cycles are used and junction temperatures are dominated more by the thermal_resistive divider from junction to ambient and will be higher or much higher. As a rule of thumb it is almost always safe to assume that worst case Rdson will be no more than twice the 25C value. In some cases it is close to double and in other cases maybe only 20% more so datasheets need to be checked. Note that data sheet tabular values are "typical" and NOT "worst case" unless otherwise specified. Top manufacturers may provide typical and max values. Design MUST always use worst case values.   

Data sheet graphs almost always give a single value for the parameter set involved and this must be assumed to be typical unless otherwise stated. eg a set of curves may be given showing Ids against Vds for a family of curves at various Vgs values. To show worst case and typical values would need addition of error bars or twice as many curves and I've never seen either done. 

Junction temperature and acceptable max I values under various pulse conditions can be found in many data sheets from a table designed for this purpose. This can be useful for push it to the limit designs but usually for on/off switching designs assuming dissipation of Rdson x Ix^2 perhaps a duty cycle if &lt;&lt;1 is usually safe and advisable. Here Ix is some magical figure between Imax and Iavg. Using Iavg may be safe for a Ids range that is usually about the same most of the time but as dissipation is proportional to I^2 using I average may be risky for cases where peak I and average I differ substantially.   

Example: Given an Rdson of 0.1 Ohm and 0A or 10 A current at 50% duty cycle.
Iavg = 10A x 50% = 5A.
Dissipation using Iavg is
Iavg^2 x Rdson =   25 x 0.1 = 2.5W
Actual = 10A^2 x 0.1V x 50%  = 5 Watt
= double value using Iavg. 

Steady state. junction temperature = Pd/Rth_total
Rth_total = Rja = sum od thermal resistances from junction to ambient.
Main components of Rth are
Rjc = junction to case thermal resistance +
Rcs = case to sink  +
Rsa = sink to ambient thermal resistance.
So Rthtotal = Rja = Rthjc + Rthcs + Rthsa  

Rjc is usually designed by the manufacturer to be "sensibly low" such that junction temperature is not too high above case temperature as full power, giving the designer a fighting chance of getting rod of the thermal energy at full dissipation.  

At more than trivial power levels it is usual for junction temperature to be in the say 60C - 100C range in continuous use and values of 120C or higher may be acceptable. While notionally a device may be operated at up to the Tjmax value of, typically, around 140 C, this leaves no headroom for thermal transients and begins to have affects on device lifetime. [Cree specify their lighting class LEDs for operation at Tj of 85C and 105C and often no longer give 25C Tj figures in datasheets]. 

Vgsth - minimum gate voltage for turn on.  

The MOSFET has 5V available for gate switching when your boost converter is operating but it is safer to start with a device that is at least half happy at the minimum of 3V available from a minimum voltage LiIon cell. So start with a Vgsth of well under 3V if possible.
Vgsth is the "just turned on" Vgs so lower is needed so start with a 1V to 2V Vgsth figure. Values under 1V are fine if available but are very unusual and almost always are also associated with a lower than usual Vgsmax value indicating an extremelt thing gate oxide thickness and potentially added sensitivity to electrostatic damage.

Selection:

That should do for a start. We could have looked at case type (do you want to solder QFN pkgs?) or power dissipation (unlikely to matter here), or ROHS (RO what :-) ) , or ... . In cases of high switching rates losses from gate charge/discharge may become significant and we may start looking at junction charge values and ..., but in this case and for most 1st passes such details can follow later if needed. 

I personally use Digikey as my first choice component search engine due to their utterly vast listing base, good (but not perfect) parameter driven selection, knowing that if they stock it the brand is almost certainly reputable (and if you buy from them its probably genuine). I also sometimes actually buy product from them :-)/ (I'm in NZ so if buying for use here shipping costs can matter). There are many other supplier systems that can be used in this manner.  

Set Digikey (or other supplier) selection system filters (one at a time is recommended) to:
MOSFET,
PChannel,
Vds >= 20V,
Ids  >= 1A,
Rdson &lt;= 100 mOhm
Vgsth&lt;= 2V,
in stock &lt;- usually desirable
quantity 1 or more  &lt;- higher minimum usually gives wider range and lower prices  

Yielding 35 devices for Digikey in this case. 

Potential candidates

Sort by $ ascending to start.
All else being equal, lowest cost is nice.
Later, reordering by eg Rdson and Vgsth can be informative.
Near the bottom for low cost is Panasonic MTM761230LBF at $US0.35 /1.
Despite having an annoyingly small pkg I'll comment on specs in some detail as they are 'more special than some' in good and bad ways.
Product pricing page here
Datasheet here
This is in a mini 6 SMD pkg that is harder than some to solder but doable.
4 of the 6 pins are drain. making soldering much easier than if they eg placed the gate connection between two other terminals (as some do). 
This is a 20V 3A device - acceptable in this application. 
Rdson = 36 milliOhms - nicely low.
They say "2.5V drive". As Vdrive useful is >> Vgsth the Vgsth must be low. It is.
Vgsth = 0.4/0.85/1.3 V min/typ/max = VERY low and
Vgsmax is only 10V as a consequence (see discussion above). This is acceptable as long as it is realised and designed for. As Panasonice 'know their stuff' as well as most you'll see from the datasheet diagram  that there is a bidirectional voltage clamp on the gate. This is highly desirable in devices with such a low Vgsmax. Without such the merest whiff of electrostatically induced voltage can destroy the device. With the protection you still should treat them with due reverence. 

At 1A with 2V on the gate it drops 0.05V Vds - this will be higher when/if hot but not more than double = 0.1V.
as you have now said that Iload max is 100 mA this will be very acceptable. (Surge current may well be rather higher but easily handled)

If desired, a much to solder part costing 56c/1 and rated at 30V 24A and 25 milliohm is the St STD30PF03LT4. While Vgsth is specified as 1V min this is misleading - it really, really wants 3V to get going half well.
It's in a large enough to see and hold and solder DPAk.
At 24A Ids it's in a different class than the lovely but more fragile Panasonic part. Both would work here - especially if close to 5V drive is used for the St part but even at 3V.
Pricing page
Data sheet 

For a small and adequate solution see the 49cents/1 SI2301.
Only 20V 2.8A (adequate), SOT23 pkg, and slightly over the 100 milliOhm on resistance spec but probably very happy at 2V on gate and probably rather less (the graph gets too hard to read).
Datasheet

THE POINT HERE is not so much the specific parts we have arrived at (and quite a few more) but the method of choosing important parameters, whittling the options down by setting the desired parameters to >= the minimum acceptable value (eg Vds) or &lt;= max acceptable value (for eg Rdson) and progressively
homing in on parts that meet the spec. If potential components ~= 0 then specifications can be inspected to see which ones can be loosened.