Qualifications
"A Senator must reach for noble qualities—honor, total dedication, self-discipline, extreme selflessness, exemplary patriotism, sober judgment, and intellectual honesty." —Senator Robert Byrd, the longest-serving member in Senate history.
Remember, he said reach for; you don't actually have to grab any of it. It's not your fault if you don't have the arm length to get there.
The legal requirements to serve as U.S. Senator are easy to find. They're written in a little document you may have heard of: The Constitution of the United States of America. We really hope you've heard of this thing.
The first qualification is your age—you've got to be at least thirty. There's no maximum requirement, so technically your Great Aunt Alice could still run, even if she can't read the bills she's voting for. Next is your address—seriously.
You've got to at least have a home in the state you're running in (this is more complicated than you'd think). Finally, you must have been a legal citizen of these United States for at least nine consecutive years before being elected.
And that's it. You can be as introverted or panicky or anxious or moody or obsessive-compulsive as you'd like, and as long as you pull in more votes than the other people you're running against, you're also going to be a leader.
Senators come from a variety of educational and professional backgrounds. Some are lawyers, some are business owners, others are doctors or public officials or university professors. There's even been a guy who specializes in horse hooves—in the 21st century, no less (source). A few are career politicians who started in state government or the House of Reps.
While just about every senator has at least a college degree, there's no education requirement in the Constitution. The question is whether you can get elected without one. You can—but you probably won't.