Working lots of short-term contracts are fine when the economy is good. But when the economy goes bad, you'll see those contracts dry up very quickly. Then you're looking for a full time job along with everyone else who was doing short term contracts at a time when companies are scaling back hiring. Most of you are going to have a bad time.

A full-time job offers some protection from volatility. I'm not going to pretend that nobody has ever been laid off from a full-time job, but if you work contracts you have ZERO job security. And contractors are the first thing to go in cost cutting mode.

If you go the independent contractor route, make sure your emergency fund can cover 18-24 months of expenses. Also, recognize that while the pay may be higher, if you're in the US you also are on the hook for 8% payroll tax that your employer would normally pay on your behalf.

If you go this route, you need to adjust your definition of "well off". If you are looking to keep pace with your friends working at Google and making $150k, that's pretty unlikely. But you can probably pull $60k and still meet your savings goals, and $60k/yr is more than enough to live comfortably on. And that number won't be static; some years you might make $100k and some years you might make $20k. You need your savings to be able to survive the lean years.

All that said, based on your comment I assume you have no work experience. Why would you hire yourself for a short-term contract over someone else? Go work somewhere full-time for at least a few years until you have a good answer for that question. You almost certainly have a whole lot of tradecraft to learn as well. Once you've built up some experience (and some contacts) you can think about contracting.