OP get a used 1000 series PSP with a 8,16 or 32gb sony branded SD card and install custom firmware on it, you can play anything from gameboy to GBA to snes to Ps1 games on that and it is very cheap to obtain (I bought my PSPs for 60 CAD at the flea market).
It costs way less than those garbage handheld emulator machines and is way more powerful.