Out of a PA28, PA28R or C182, I'd chose the 182 hands down for your trip.
Firstly, you'll have extra shade due to the high wing, which is a must this time of year.
Secondly, you'll have at least 100-150 litres of extra fuel you can carry, depending on the 182 you pick up. That will give you much more choice when it comes to refuelling, and help you avoid the places that cost $2.50-$3 a litre.
Finally, with the high wing you'll be able to get a better view and some great photos.