Honestly, if you wanted a good camera, I would rather go for a dedicated option as those have far better image quality due to much larger sensors + lenses. There's a lot of good small options that are relatively affordable, like many of Lumix's M43 cameras (particularly the older ones, like the GX800/850) or some of the older Fuji bodies if you prefer something like that. Sony themselves have really solid cameras too, the A6000 series is excellent and nearly all the same (main differences are IBIS for A6500 and up and newer sensor + software UI on the A6700), a lot of people recommend the A6000 as a solid budget pick. I personally use the ZVE-10, which is basically a plastic body no EVF version of the A6400 (which has a metal body)

Sony's E-mount, Fuji's X-mount, and Panny and friends' L-mount will all give you lots of good third-party lens choices. I would stick with M43 and APS-C purely because of the size difference compared to full frame. Sony and Fuji have APS-C options while Panny has M43 ones that are even smaller. The most notable size difference is definitely the lens, M43 lenses can be very tiny!

If you want some content to watch relating to fun budget cameras, I would recommend Micro Four Nerds (mostly covers Lumix and Olympus), Mark Wiemels (covers budget lenses and APS-C cameras), and Mark Bennett's Camera Crisis (funny guy who likes a good deal, he's a comedian who likes cameras as a hobby)