Mine was the Game Boy Pocket. I don't remember enjoying it too much though since it kind of sucked though that may be because of the types of handhelds out today which could be skewing my memory a bit.
Game Boy Color. Before I had it, my sister had a Game Boy Pocket and I was jealous, but I got the better one. I think it was blue (like my DS Lite now), and I have no idea whatever happened to it. Thank god I never lose anything anymore.
My first handheld console was a purple Game Boy Colour which I got with Pokémon Red version. I still have it but the start button is not working. I use my original Game Boy Advance and GBA SP for my Game Boy Colour games now.
Well the first one I ever played on was my sister's lime green game boy color, but the first on I owned was my blue Gameboy Advance SP. Still carry it around since the DSi doesn't have a gameboy advance slot.