I have a retro pi that lives always connected to my tv for impromptu play like you describe.
The Analogue OS doesn't say if it supports TV output or controllers besides
> OS is designed to connect seamlessly to virtually every 8BitDo Bluetooth, 2.4g and next gen controller. Wired and wireless. With button mapping on a controller by controller, system by system basis.
I attached two cheap USB NES adapters to it, allowing NES controllers of all kinds to be plugged in.
It works perfect for contra, battle toads, tetris, whatever, and feels extrememly close to native form my experience (which is impressive to me, as I used to play competitive NES tetris, which requires 1 or 2 frame input windows for some techniques)
EDIT: And TBH if that format is best for you, why not just spend your money on a real console instead? It'll definitely be cheaper and will ALWAYS boot faster than anything else you can buy.