For cheap, I'd suggest the Pocket Go, [1] but for my favourite I love the RG350P, [2] which is a little more expensive but has a community with a lot of homebrew behind it and it can run pretty much anything from PS1 downwards. There is also the RK2020 [3] with a little more oomph than the RG350P, the RK2020 is a pretty brazen Odroid-Go Advance clone, so if Odroid has the Go Advance in stock, get that instead, but they rarely do.
If you find these just a touch too expensive, they can be found on Banggood for small to hefty discounts. I got my RG350 (not RG350P, the RG350P is a minor improvement over the RG350 but at around the same price) for $60 on Banggood. Also, expect 1-2 month shipping on these consoles, but in my opinion it's so worth it.
[1] https://retromimi.com/collections/handhelds/products/pocketg... [2] https://retromimi.com/collections/handhelds/products/rg350p [3] https://retromimi.com/collections/handhelds/products/rk2020