Your auto club should be able to provide you with maps, and it could also get you some discounts at places like motels.

Some national park campgrounds will have showers - sometimes pay showers - others won't, but rangers can usually direct you to places outside the park they are available. The National Parks website will have all of that information available for you. I find that state parks actually have showers more often than National Parks/Forests.

T-shirts won't be hard to find. Most parks have a visitors center or book store where they'll sell shirts and other souvenirs, and they're usually not priced too bad. Stores just outside the parks will frequently also sell stuff, that may be cheaper, but it can be of lower quality.