So you wanna be a "trailer sailor"? Good for you! If you have the place to store it, then you just saved yourself a significant portion of the cost of ownership. I own a 25' boat, and I pay ~$2500 a year just in slip fees and putting on the hard in the winter (I sail on the Chesapeake Bay just north of Annapolis). After throwing in the "everything else", owning a boat this size costs me about $3500 - $4000 a year (Mine has a motor, though).
You could go with something like a flying scott and probably stay within your budget. A big decision you need to make is if you are going to have an engine or not. I'm not sure where you sail, but personally I think having an engine is responsible as it can get you out of trouble quickly and easily should the need arise. I prefer being a little overpowered vs. underpowered. So a 5 or 7 HP outboard ought to do it for a 22' boat. I have a 10 HP on my 25' (4500 lb displacement). The outboard alone will run you about $600 - $800... It adds up quick!
As for getting a license, check you local guidelines. The coast guard regulations say that you need Captains license (100 ton Master or Limited Master) or "six pack" (OUPV) ONLY if you are going to be taking people out who are paying. If you are sailing recreationally or with friends, no license is required. http://www.uscg.mil/nmc/faq.asp . Having said that, you should certainly take a boating safety course and understand the "rules of the road" before you go out on the water without someone more experienced. You can take classes with the ASA and learn a lot from basic keelboat to coastal cruising. http://www.american-sailing.com/
If you're just interested in day sailing, you may want to consider a catamaran. A 16 or 18 foot cat will cost you about $2000 and you can fit 4 people on it. Cats are FUN - with less displacement, they sail about 3X faster than monohulls. They are the "motorcycles of the sea". I own a Prindle 16 that I keep at my Uncles house on his beach and LOVE it!
One word of warning though: sailing is ADDICTIVE! You are going to find your self looking at bigger and better boats, doing those calculations in your head, etc... just make sure you are responsible about it. Don't buy more than you can handle. A 22' or even up to a 27' is a very good starting size. I would go for tiller steering vs. wheel because need to develop a feel for good sail trim and the tiller facilitates than more readily. I grew up sailing, and learned on a wheel so I've actually had to re-learn a few things as a result. Go with a tiller at first.
A good way to get experience is by racing. I race with the Annapolis Yacht Club. I'm not sure how it is where you live, but when I first started racing, I just showed up on the dock with my gloves and case of beer and started asking around. Before I knew it, I was a permanent crew member with a great bunch of people.