Alright, great choices! First off, if you're looking for an all in one solution, retroarch is an emulator front end that then uses cores of other existing emulators, and you can just download everything at once. I don't actually recommend this, because the interface is controller focused and the settings aren't super intuitive to change, but the option is there.

For GBA, mGBA is well regarded and feature rich (it's got settings for, for example, boktai's solar sensor or megaman battle network 4.5's battle chip gate).

For DS, I've previously used desmune, but the consensus seems to be that MelonDS runs much more efficiently.

I haven't run much 3DS emu myself, but I've heard good things about azahar since citra was shut down.

Finally, PS2 the obvious choice is PCSX2, though setup will be a little more complicated. Specifically you'll need to obtain and install BIOS files which ARE Sony proprietary property, and as such not included with the emulator. Internet archive has them (show all > PS2_BIOS.zip > misc bios starting with ps2, depending on your desired region).

I will say, the GBAs low cost of development means the library is full of hidden gems and I highly recommend exploring it. Personally I was a big fan of the Summon Night Swordcraft Story games (make your own weapons with a variety of fighting styles), Kojimas lesser known GBA game Boktai (1, for a variety of reasons, a game about fighting vampires with a solar powered gun), and Astro Boy: Omega Factor (a wonderful beat em up by the much beloved Treasure), though that's just a few with more of an action focus. If you're looking for reccs in a particular genre, feel free to reach out