So, i'm making my second ever hobby robot(I'm 15) and am planning on soldering my own connectors for the battery, sensors, Arduino, etc. It will be a small mobile robot. Anyways, I was wondering what a good gauge of stranded hookup wire would be good for that purpose. Thanks!!
For power/ground/analog signals the only limitation on how small you can go on wire gauge is power loss. You can look up voltage drop calculators online but generally speaking if it's short runs with low current you shouldn't run into problems with wire gauge being too small. One place where you do need to be careful is when using ratiometric sensor such as rotary potentiometers or resistive temperature sensors as the resistance of the connecting wires could have a measurable effect. In the applications I work on I use a rule of thumb of 28AWG for signals, 26AWG for low current devices (up to 0.2A) 24AWG for up to 1A and 22 AWG up to 3A (assuming the lengths aren't more than 1-2m)
As much of a consideration as wire gauge is the wire material and protection. Plated wire (normally tin) is much easier to solder, I've occasionally had batched of unplated wire which refused to solder unless attacked with flux and steer clear of wire with thick PVC coating. Not only is it bulkier but the PVC melts when you solder the wire.
You may want to check this table to see what a given AWG size can handle in terms of current as well as AC frequency.
Remember that getting enough surface area on your connections is as important as using the correct wire size.