Having the menu being usable with 1-button is waaaaay better for sure, if you can do it =)
It's very difficult, though, to implement Escape and Pause during the game with one button, so feel free to keep Esc to quit, and something like P for pause or whatever.
The 1-button rule mainly means that :
- you can play the game just by hitting/holding the same key ;
- several keys can be mapped to this unique button for better comfort (space bar, LMB, X on a gamepad... all could trigger the same thing).
As for the onscreen button, well...
There's no mouse mouvement in such games, so a "clickable" button is off topic. But you can have an interface with several buttons. For example, a simple tap on your key moves to the next UI button. Holding the key activates the current UI button, etc.