There's no methodology for this kind of things, only practices that can be damageable for your game or boost the retention/revenue/add your KPI here.
It depends on your game, if you're playing an Arcade game (like Temple Run), the player will only "Play", "Replay" and "Scoreboard". Of course, depending on the complexity (let's say, Jetpack Joyride), other buttons and sub-menus can be added.
The question you have to ask yourself is : "What can my users do?" and then "At which point will they do it again?"
Imagine in Temple Run if you didn't have this button "Play again" when you died, the game would be less sucessful (you died => Want to win => Game propose you to try again => You try again). You have to think about the path your user is taking before, after and between each game to say "Ok let's put this button here".
More importantly : TEST. If you see that the button "Play again" is not used : Why? Is it because people play only once and then come back later? So let's try another button "Gain power by playing another game right now!". (of course, some UX writing has to be done here).
Please, avoid those "Pop-up" microtransaction. It'll frustrate the player more than anything else (I mean, who wants to be disturbed while playing for paying?). Try to find a way to implement those options directly into their traditionnal path when they play your game.
Exemple : Jetpack Joyride has a good way of implementing this, while Assassin's creed Rebellion tends to show you 2-3 pop-up and it's really annoying.
And again : TEST. Maybe putting pop-up screens for offer will boost sells and does not decrease retention?
If something is not clear enough, don't hesitate. Mobile games are really a fun field to work as an UX designer and you have plenty of creative way to implement innovations!