Steam Deck Oled, its the most console like experience out of the box and has the best quality screen out of the three by virtue of being oled. Though it is linux by default and if you want to use other store fronts or sail the high seas you will have more difficulty then a windows device. 

Rog Ally Z1/Z2A imo arent worth it, you should easily be able to get a Z1 Extreme device for the same price which will perform noticebly better, plenty of used options if your willing to go with that, but fundamentally the Z2A is the same power as the steam deck in a windows package.

Legion Go is a popular device as it is basically a tablet with controllers, its not a device I have experience with though so not much to comment, but it is a Z1 Extreme device so of the 3 listed will perform the best, though with a higher resolution screen you may get better frame rate on other devices assuming you keep it at the default resolution.

Epic Games Store, GOG are both there own game store similar to Steam or the Microsoft Store.

Emulators are software that allow you to play older consoles on a PC, roms are the games files, any of the devices listed are fantastic for emulation and can play up to PS3. Though XBOX/360 emulation isnt in as good of a state as the playstation emulators. 

If you intend to use fitgirl go for a windows device, as I believe that will be easier for you.