Wiring a shed/workshop
TLDR

Use THWN-2 #12 stranded wire.  

Use six wires: black white red blue gray and green/bare. 

Green/bare is ground for both circuits.  

At the ends (once they are installed) wrap the black/white/red with electrical tape to group them.   Also wrap the blue/gray.  

On the lighting circuit, gray is neutral and blue is hot. No need for GFCI here.  

On the outlet circuit, white is neutral and black and red are both hots. Cap off red for now on both ends.  If you're not doing GFCI, get a 2-pole breaker (handles tied!) and punch the black down on one side and don't use the other yet. If you do GFCI, get a 1-pole for now because 2-poles are expensive. The red wire is there to make it legal, and gives you a spare circuit.  

You can't run two of the same type of circuit to an outbuilding.

So you can't have two 15A 120V circuits to the shed.  Nor can you have a 15A/120V and a 30A/120V circuit (e.g. for a travel trailer) - the amps are different 

However you can have two different types of circuits: 


One 15A receptacle circuit and one 15A switched lighting circuit
One 15A receptacle circuit and a 240V utility circuit
A 240V compressor circuit and a 240V pump circuit because the pump is switched on/off by equipment in the house
One 15A receptacle circuit and a 120/240V multi-wire branch circuit providing two 20A subcircuits


For instance I would run a 20A multi-wire branch circuit providing two legs of 120V that you seek. That counts as one circuit for the above discussion.  However, this requires a circuit breaker that would most likely common-trip, so you'd lose the lights when the saw tripped the breaker. If that's what you want, then you may want to consider a MWBC for the power (strictly to avoid the same-circuit requirement) then a plain 120V circuit for lighting.  

Another option in the LED age is to use 240V for lighting.  

Wiring

Wiring wise, since you are in conduit, you run individual THHN type wires (actually THWN-2 but they'll be cross-labeled).  For instance in an MWBC, you'd run black-white-red, and for a 120V circuit you'd run blue/gray.  (gray is a neutral color). 

1 ground large enough for the largest circuit; you can share grounds because you're only expecting to have a ground fault on one circuit at ta time. 

Subpanel

If you foresee any need to expand beyond that, then you should install a subpanel in the shed.  I gather that you have a 60A subpanel next to your main becuase it is full. Also, 60A implies it is very small in terms of spaces, so it's a stop-gap, not a long-term solution.

We preach "you want lots of spaces" pretty loud around here, so if it were me, I'd replace the 60A with a much larger panel in terms of spaces. I'd aim for 45-ish spaces in a typical house.  So if  your panel is 24 space, 18-24 space is good; if 16, aim for a 30-space panel.  Then move the old 60A subpanel to the shed.