There are a lot of buses shuttling between Puerto Iguazu, the falls, and Foz do Iguacu. I wouldn't bother renting a car.

Foz is a big concrete Brazilian city, not particularly attractive. Puerto Iguazu, the small city on the Argentine side, is much more pleasant, and also much cheaper.

As for visiting the falls themselves, I'd start on the Brazilian side. It offers the best panoramas of the entire site. Then I'd cross to Argentina, and spend the majority of the time there. This is where you can get up close to the various falls (there are dozens of separate ones) - the Argentine park has catwalks all over the place. In many places, you can reach out your arm and have the falls run over it. The highlight is the catwalk that takes you directly over Garganta del Diablo, the main drop.

You will get wet, probably very wet, on the Argentine side. Bring plastic bags to keep your camera and any other electronics. There's an inexpensive boat that does tours at the base of the falls, worth checking out. You'll also see bands of coatis (long-tailed raccoon-like creatures) patrolling the park.