I've found that Game Boy games are usually not very good.
I bought an Analogue Pocket machine and downloaded an archive of ROMs from archive.org and the only game I've found myself playing from time-to-time is Tetris.
Am I missing out on something? I've tried the Pokemon games but even those seem... well... boring.
The Wario Land games are fantastic. Kirby is good. Mario Land might hold up? There's three Zelda games on the Gameboy Color that are worth playing as well. It's honestly not the strongest lineup of games, but there's some bangers.
Any system that can play Mario, Zelda, Metroid, Pokémon, Kirby, Kid Icarus, Mega Man, Castlevania, Harvest Moon, "Final Fantasy" (Adventure/Legend), etc. sounds pretty good.
There's always GBA though if the original handheld versions seem too primitive.
The Pokemon games were revolutionary at the time but they have all been remade at this point. I'd recommend Heart Gold or Soul Silver, if you don't like those you'll never like Pokemon.