As far as running a 32-35mm tire you'll be completely fine. Even the narrowest rims I've come across will fit tires like that no problem.
A far as strength is concerned, that's going to be a function of your weight and how you use the bike. Not the tire size. I wouldn't recommend lightweight 18/24 spoke wheels for commuting but you might be ok. In any case, any issues will not be caused by the wider tires.