The Retroflag GPi case allows you to build a retro gaming handheld with a Raspberry Pi Zero (I recommend Pi Zero W). Assembling and configuring the software (RetroPie, Recalbox or Lakka) is pretty straightforward. Also, it runs on AA batteries to complete the retro gaming experience.
I picked up one of these last week from Core Electronics for ~$113 + shipping. At $95 + shipping (~$7), it's a pretty good deal.