OK, a 30 footer will be doable on $5000, but most likely it's going to be pretty old and in rough shape. Take a look at some Catalina 27's. Even dropping down to a C-27, it's going to be hard to find anything halfway decent on $5000.
I think you will be pleasanty surprised as to how much room a C-27 has - Way, way more room than the 21 you looked at. Full standing room and a compleately enclosed head, probably with a shower. Enough room that you can have 2-3 people comfortably spend a few days with you.
Yes, take your time, look at a number of boats, take pictures and note the plusses and minuses of each.
As far as classes go, as mentioned, you will most likely need, at least, a boating safety class. After that, both the US Power - Sail Squadron and the Coast Guard Aux. offer seamanship classes and more advanced boating classes. Yes, a hand's on sailing class will be good, but it's going to take a big bite out of your budget..
When you do find a boat that looks like the one to buy, make sure you find a good, marine surveyor to do a full survey on the boat. A survey is going to run you anywhere from $15-25 per foot depending on the skill and experience of the surveyor. Part of the survey will have the boat hauled to check out the bottom of the boat. That's going to cost you another couple hundred dollars. If you think you can pass on the survey, don't. Surveyors often find problems that could cost big bucks to fix. Also, if you plan on insuring the boat, no insurance company will touch it without a survey report.
When you find a boat that looks interesting, don't hesitate to post it here and let other members give you their 5 cents opinion on them.
A few months ago, another newbie came on here looking for advice to buy a boat to liveaboard and do some traveling just like you. We exchanged a number of posts and emails and ended up, I actually found the boat that he ended up buying. The guy is happy as a clam.
You say you don't want to live at a marina, but instead, want to anchor or hang onto a moring ball. If you do that, have you looked into getting some kind of a dinghy to get to and from shore with?