Best practice when choosing a trim pot value
Normally you want the adjustment to accommodate the worst-case variability and not too much more. In other words if you add up all the worst-case tolerances of the reference setting and it might be +/-100mV off from your nominal 3V setting, you might allow adjustment from 2.85 to 3.15V. Since potentiometer element resistance generally has a lousy tolerance you would prefer to either connect it across a "stiff" voltage or parallel the element with a precision resistor. 

In my hypothetical case, suppose I have a 4.096V precision reference, I might use a 10K pot and parallel it with 301 ohms so the divider current is 1mA nominal. Then the divider would look like this: 







simulate this circuit &ndash; Schematic created using CircuitLab

The source resistance looking into R1 wiper varies by +/-1250 ohms as the wiper 
is moved. That's not a problem in many situations but you should be aware of it. 

General rules- 


Do you really need a trimpot or can you do it digitally? It's 2020, 
dude, what are you thinking?   
Avoid using potentiometers as rheostats wherever possible, minimize current through the wiper. If you must use a pot as a variable resistor, tie the unused end of the
element to the wiper. And avoid use of &lt; 100 ohm cermet pots as rheostats because of contact resistance variation.  
Use medium resistance pots were possible, especially if you need a wirewound
pot. Usually 2K to 50K is optimal.  
If your adjustments are interactive, design your circuit so that at least one of the pots is nominally independent. It's worth extra care and even a few extra     parts to minimize iterations.  
Make the pot rotations "make sense", 
generally clockwise should increase what the technician is
observing.