Potty training?

Rainbow
My 2 year old has decided she's ready to potty train! We've had a potty in the living room for about 5 months. She's just been sitting on it for fun and occasionally peeing on it until today! She took her pants and diaper off by herself and sat on the potty and peed. I left her naked and she's since then peed on the potty on her own without me telling her to 4 more times. I'm so excited! But now I have some questions. 
What do I do as far as diapers? Do I put her in undies at home or all the time except night time? I have a travel potty to keep in the car for outings. Should I put her in a diaper when we go out? 
Also, she's peed in the potty 5 times in the last hour. I'm telling her good job and getting excited every time so is she doing it a lot because she thinks it's fun to get me excited? Or does she really need to pee that often?