Well, if you're trying to go as fast as possible, then aero wheels make a lot of sense. Personally, I don't quite know why the "personal best" riders aren't all mounted on time trial bikes with disk wheels, aero bars, and the rest of it.

If you're just out to enjoy the day, and don't care that you will end up a few minutes slower to the finish line, then the wheels don't matter as much.

There is an argument that aero wheels may not hold up as well as traditional ones. I think this is probably true for some of the ultra-low spoke count, trick lacing pattern, etc. wheels, but can't speak to the carbon multispoke wheels because I have rarely used them on the road.

Tires? Narrower is more aerodynamic, essentially without exception. You have to balance aerodynamics, weight, rolling resistance, comfort, puncture resistance, and longevity yourself, though.

Fun, eh?