Hey all I have a simple question that I haven’t been able to find the answer to.

What gauge wire would I need to purchase in order to solder a wire to some places on an iPad mini?

The area looks like this:

Originally I was thinking that 30ga would be fine but I’m not sure.

 

30AWG is ok.
You have a choice of plastic insulated wire-wrap wire or heat sensitive enameled copper wire. In the latter case, the heat from the soldering iron will melt the insulation and hence no stripping is required.