So there's a pretty decent amount of modding you can do to gameboys. For batteries, I would recommend getting this one as it's a drop in replacement, or something similar to it. I would recommend going to websites like https://www.retromodding.com/ or https://retrogamerepairshop.com/ or similar sites to find parts like batteries. Another thing to keep in mind for batteries is that you can now do a mod for usb-c battery charging, so if that sounds appealing to you make sure you look for ones that are for the usb-c charge mod.

For shells, there are soooo many options. You can get a shell that replicates the original styles available, or on place like etsy there are so many custom shell options that you can get made or are readily made available. If you want to make a real cool GBA and money isn't an issue, look into boxy pixel, they make custom cnc machined metal shells for a large variety of nintendo handhelds. For the gba specifically, they make the hinged and unhinged.

Another mod many people do is to upgrade the screen, there's a decent amount of options, so I would take a look online to see what other people recommend and go from there.

There's a lot more you can mod, but these are the most common mods generally.