The engage window is based on his W. It has a long early cooldown, and is the only real thing you should be concerned with when deciding whether or not to trade. Letting him waste Q or E on minions is helpful, but not necessary.
Also don't even think about considering his pre-11 passive, it does pretty much nothing.
Now, if you would like to list some champions you play, and what ones you would prefer to play against him, there are a number of Garen mains on the boards that would be happy to help you out.
EDIT:
he heals in battle with minons
What? Would you mind explaining what you mean here? The only thing I can come up with is you are referencing Grasp, but that is only maintained by hitting minions, it doesn't heal him until he hits you.