Push the ball: Push the ball has a neutral Focus, so a man to man defence fits best. But if one of the teams is unbalaced, also 2-3 or 3-2 Zone could be the best. For examble your team has great outside defender but weak inside defenders, so you could get a balanced defence with 2-3.(i like to switch for 2-3 more then to 3-2 because of the rebounding)
Full court press: How to counter an FCp with a special tactics is a good questions, prbadly i would go for push the ball or look Inside(normally there are many points under the basket against a fcp even with outside Focus strategyies like run and gun) ... But if your team better in shooting outiside also run and gun could be a good choiche against the non existant defence.
More important is to have good Ballhandlers and Passers in your Rooster, if you line up center with this skill one or 1-2 there could make 10 TO in that game and that is hard.