I picked up a steam link when it was on sale for about $20, and use it to run about thirty to forty feet (one room over)
I've had really good luck with it, and my internet isn't great.
It's choppy on wifi, but if you have Ethernet and don't expect it to look as good as your pc it'll work fine.
I don't play any fps or twitchy games though, so I wouldn't be able to comment on that