I brew completely inside in my kitchen. There are a couple of pictures in my gallery. I do have a fantastic stove that can easily boil 6.5 gallons, though.
For any beginner, though, your kitchen is adequate. You may want to continue to do that. There are plenty of experienced brewers who only use their kitchens, and have no desire or need to go "bigger and better". I'm a little obsessed, though, so I'm always thinking about somehow getting more stuff!