I can't advise on rental outfits at Vegas, but a little C172 should be good for crusing over the Grand Canyon.
I rented a C172SP (180hp) in September, with 2 up, full fuel (51 usg) and plenty of bags (all within W&B) we had no bother getting up to FL105 at above ISA temperatures. You'll need the special chart for the canyon that has the routes specified.
If you are unfamiliar with high altitude take-offs get some instruction on your check ride.