If you have $600 to spend, then a Contend or Trek 1.1 would be a great starting place.

Claris shifters and components function perfectly well. YouTube will tell you how to keep them adjusted and working properly.

WHEELS:

1. Most likely, if you just ride somewhat carefully and don't do curb jumps or potholes or speed bumps too fast, you wheels will hold up fine for awhile.

2. In the case that you find out that 250lbs is too much for the wheels, you an easily find a stronger (more spokes) wheel or wheel-set for around $100-150 when the time comes if you aren't concerned with getting super-light wheels. (this could be an option if the need arises: Vuelta Corsa HD Road Wheelset)

But I wouldn't worry about it until something happens. The simple fact is, you could spend 2 or 3x your budget and still not get much more durable stock wheels on a bike.

Also, if the prices are comparable...the Trek looks like it has a carbon fork, if that makes a difference to you...if you can test ride both, that's ideal.