the absolute best handheld emulators are (IMO)
AYN Odin 2 (£220ish) Android so anything up to PS2 with a good amount of switch
Steam Deck (£200+ used, OLED £479 new) Steam OS, can play anything up to & including some 360/PS3, Switch etc
Retroid Pocket 4 (around £170 shipped) Android, lower spec than ODIN 2 but will still do everything up to & including PS2
if your looking for something cheap to play old school up to GBA/PS1, Miyoo Mini Plus or Ambernic RG35XX are probably your best bets.