With a budget like that I would skip most of the extras we all like to have. Gloves, bottles, shorts, etc. To get started you really just need a lock, a helmet, and a way to put air in your tires. If you ride for a while first you will be better able to choose the right stuff for you when you are ready to spend more money. Do you really have to travel 3 hours to get to a mechanic? I hope you are good with your hands.
Welcome!