I was looking to use one of my cheap electric guitars to use as an experimental guitar (try different gauge strings and different tunings). I don't know much about setups, so I was wondering if there was such thing as a setup that could be used to lock in the guitar so well that I can keep putting on all different gauge strings without it constantly going out of tune/bending?
The only real set-up issue I can think of for string gauges is intonation. The rest should stay in the same place depending on your climate and how often it changes. People will argue you need to adjust your truss rod every time, just check it every string change and you shouldn't need to make any adjustments should you get it right the first time.
The only things that would really matter are keeping the pickup height adjustment a reasonable distance (approx 1/8") from the strings, & don't use a tremolo bridge like a Floyd Rose. Use a fixed tailpiece/bridge, otherwise you'll have to constantly re-adjust the spring tension on the bridge. Also, if you have the action set too low, you may get some string buzz as you increase gauge size.
People will argue you need to adjust your truss rod every time, just check it every string change and you shouldn't need to make any adjustments should you get it right the first time.
if you've changed gauge it's a good idea to check again after a few hours to see if there's any change in the neck relief. it might not do anything if you're just changing from 9s to 10s or something like that, or it might take a little while to settle and then only move a tiny amount that isn't going to cause any problems. for extreme changes the truss rod will pretty much always need to be adjusted, though.
I've always had more issues with neck relief than intonation when changing string gauges.