Well, one of the reaons why classes usually contain private members with public getters/setters is exactly because they can verify data.
If you have a Number than can be between 1 and 100, i would definitely put something in the setter that validates that and then maybe throw an exception that is being caught by the code. The reason is simple: If you don't do it in the setter, you have to remember that 1 to 100 limitation every time you set it, which leads to duplicated code or when you forget it, it leads to an invalid state.
As for performance, i'm with Knuth here:
"We should forget about small efficiencies, say about 97% of the time: premature optimization is the root of all evil."