I'd start here: https://retrogamecorps.com/2022/03/13/android-emulation-starter-guide/

Also check out his retroarch started guide, and device specific guides.

There are many options at varying prices. Depending on what you want to emulate, most phones are capable of doing ps1/n64 down. You can buy a telescoping controller like the razer kishi or gamesir pro to make the experience more handheld like. They are about $100

Otherwise, the most popular "cheaper" brands are Retroid (I have the 3+), Anbernic, or Miyoo (sold out constantly, impossible to get right now).

If you want "one device to rule them all" get a steam deck. Not exactly pocketable, but still technically a portable device, and the best price/performance.

Don't buy some weirdo thing off amazon, I recommend only the brands I listed as starter devices. There are others, but these are the best value for your money (in general).

If you want more info after reading and researching, feel free to DM me.