I only have experience of connecting flights in the states. I assume as long as you have your passport, flight documentation and visas it shouldn't be any different.
Hire cars. I hired a car a few years back and as I was going across state lines I had to make sure there was no issue. It can be apparently. Oh and fueling is a bit weird, having to pay before fueling but it's cheap.
You will need both parts of your license too.
Enjoy