Need suggestions for electric in $500-600 price range

For some background, I’m a grad student and have been learning for about 6 months now. I’m going up for candidacy and want to buy a guitar as a reward when(…?) I pass. Budget is what it is because, well, I’m a broke PhD student and I plan on buying new gear as well.

I’m a decently small person so I’m really looking for lighter weight guitars. Neck width is whatever, I’ll adapt, but I think weight being an issue will be bothersome enough that I won’t want to play it. I’ve looked into Mustangs but read they don’t hold tune well and I don’t know if 1. that holds any truth or 2. will impact my learning.

Buying new vs used is really only going to be down to what I find, not really partial to either. I know there’s good/bad/ugly opinions everywhere, but just wanted to hear some thoughts, especially how to get the most out of my budget as I’m still new.