Just like in the title, I am thinking about buying the games but I don't know if I should get it here or on steam(since apparantly the steam version of 1st and 3rd game are buggy and messy).

Mmm... Not sure how related GOG <-> ZOOM-Platform releases. But for sure Steam are based on one of them. But. With steam-related differences, DRM, bugged Steam Overlay and Steam Input and more and more (Sgeam bugged itself like hell for like decade).
Its hard to say would it be differ or not. Which ones issues you mean? Technically Non-Steam - EGS or GOG Galaxy builds - already are better. DRM-Free GOG/ZOOM even better. Just because there is no excessive overlays-injectors and drm dlls. Mathematically DRM and Steam DRM are worse by design.

But since it is old games... Their share some issues here as well. Further tweaks required. As always do. ZOOM Platform bundle their Kao 1 with degevoodoo complex wrapper. With own additional pre-launcher config tool. But game started from Desktop link as ZOOMs own pre-launcher config tool with some wrap options (windowed mode). GOG use own GOGs DX Wrapper (fork of something else wrapper) also with own additional config tool.
Both have option to force Kao 1 in windowed mode enabeld by default. I didnt try much of Kao 3 further of main menu, Kao 1 have no visible issues during gameplay part. Same as Kao 2 (on Steam too). I did try to play Kao 1 with gamepad. Its still no so responsive controls. Remind me of mine experience with Croc dilogy on PlayStation 1 (i did play them on PS1 only). Its not the port or input KB+mouse issue i assume. Especially since i play with gamepad. And already faced PS1 gamepad PS1 port games with such "wooden" controls.

Maybe still better to try Kao 1 on Sega DreamCast (or emulator for PC). Kao 2 on PS2 or as emulated Kao Challenges for PSP. And only Kao 3 was PC exclusive (assumedly, there was Nintendo port mentioned on devs website but looks like didn't reach the release).
Kao 2 in original release and in digital remades and Kao 3 have no issues in controls at least not for gamepads.

Kao 2 here same as on Steam bundled with Xinput wrapping. It is still old game. And that mean Kao 2 - and Kao 1; 3 - should be manually rebinded for your gamepad whichever device you have. No real xinput features supported - no hotplug, no wired+wireless as same device, and absolutely no default schemas even for Xbox native pads. Some issues can come of treating this old games as native Xinput ones.