I dont like handhelds and i played almost all the SNES library (arround 200 games including the most popular ones) years before i even knew what a SNES even was, you see the first PC we had at our house came with a SNES emulator installed with hundreds of games, and i didnt even knew it was a emulator i thought those were all PC games.
You should try some GB/GBA games even if you don't like handhelds. *wink wink*
How do you think i played Pokemon Red, Gold, Crystal, Ruby, Emerald and Fire Red? back in the day when i was a kid it was either beg your fathers to get you a GB / GBA or get an emulator and just play it on your PC, i tried the first option and my parents said no... so... my 10 year old self just got into the emulators and since almost everyone on school was using them we all shared the ISO files on floppy discs, no kidding we used floppy discs for the games it was actually pretty cool.