...first, welcome to the forum.
1) What would be an ideal first handgun for personal protection?
2) Is there a website where I can look up shooting ranges or is there some way I can practice shooting to get more familiar with a pistol?
3) I travel fairly frequently. I know I need a gun permit for my state, but if I were to travel between states would I need get gun permits for all the other states I travel to?
4) Also, would I have to purchase a weapon in a state I travel to or can I travel with a handgun if I declare it and put it in a case or my luggage?
1. I'd suggest you learn about handguns and shooting one, with a certified instructor, and a .22 caliber handgun. Buying handgun is like buying shoes..... you need to "try 'em on" before you buy one. If it doesn't "feel right" in your hands, you'll never shoot it enough to become proficient with it. Gun shops locally should be able to point you to an instructor. The caliber choice should be put off until you can better determine what caliber you can handle proficiently.
2. Find a gunshop, and they'll know about ranges.