There are some android based handhelds in the 200€ to 350€ range that can play a lot of emulated stuff as well as a solid number of PC indies/older titles through translation layers.

You can also grab a Retroid Pocket 5 and install Rocknix Linux on it if you want to avoid android, but it'll be more limited when it comes to playing PC games until the modding community figures out how to incorporate valve's arm translation layer.