Define what "not a ton of money" is?
Also, what skills do you have??? Can you repair what needs repairing on a boat—electrical, plumbing, fiberglass, carpentry, mechanical, etc.?
You can buy a solid little bluewater boat, like some of the ones on James Baldwin's list
, for relatively little money. Get one and liveaboard it, while working and daysailing/coastal cruising for a couple of years to build up your sailing skills and experience. Here's an example of a well-equipped Alberg 30
It would be ideal if you could get a job working at a marina or yacht club, where you could also liveaboard the boat. That would probably give you a good chance at crewing for more experienced sailors and possibly reduce the costs of living aboard your boat. One couple I know has a 38' boat and they live on it while working at a sailing school. Neither teaches, and they've both learned a lot, since they can often "audit" the classes for free.
After you've gotten yourself some experience sailing in nastier weather and learned to navigate and such... and learned the systems on your boat and how to fix what breaks... head out and go cruising for a couple of years...
I'd go with the east coast, rather than the west coast. The southern Chesapeake and parts south are not too bad in the winter time. The coast is friendlier and there are more places to sail to that are still in relatively protected waters while you're gaining experience, unlike most of the Pacific coast of the US.
Then, when you're ready to go, you can drop down to the Caribbean, and test your skills on short open water passages...and then, if you think you are interested, try crossing the Atlantic, or crossing to the Panama canal and going to the Pacific.
While you're learning, I'd highly recommend taking the ASA 101, 103, 104, 105, 106 courses or their equivalents. They'll get you a lot of knowledge in a relatively short period of time. However, without a boat and the ability to practice what they teach, it is less than useful.
Also, I'd highly recommend Dave Seidman's book, The Complete Sailor, while you're getting your sea legs back under you.
Welcome to sailnet... I'd also recommend you read the POST in my signature to help you get the most out of your time here.