As I have read this thread I thought that there is a lot of good advice but there are some things that should have been said but wasn't. To begin with, I would suggest that you need to clearly define your goal for this boat. Since you are new to sailing, I would suggest that your primary goal for the boat is to have a good platform to learn to sail and a reasonably good platform to learn to own a boat.
It should be a given that this will not be your final boat (unless you discover that you hate sailing) and that this boat will not be ideal to meet your longer term goals. But this should be a platform to learn what is important to you when you do look for a boat that you intend to own over the long haul.
And assuming that you agree that this boat is primarily intended as a learning platform then I would suggest that you look for a used but in good sailing condition, moderately
light displacement, simply rigged, good sailing, 22 to 26 foot, fin keel, spade rudder, production sloop.
Boats like these are easy to find, easy to buy, easy to resell, and will be responsive enough to teach you to sail well in as short a time as almost anything else.
If you have the boat surveyed before you buy her, and the boat is simply set up there is not all that much dramatic that can go wrong. The boat will already have scratches and so if you make a few small faux pas its not the end of the world.
Given your budget, and objectives, you are really pretty well stuck buying a boat that is 25-26 feet or less, which is not a bad thing (except that it is very hard to find a boat with 6 feet of headroom that will sail worth a darn). Even in these times, small simple, inexpensive decent sailing boats sell pretty well. Heck, your looking aren't you? Well there are a lot of folk who come here daily who are in your shoes and there will be a fresh flock of them following you when you are ready to sell. And with a $3,000 its not like you will end up paying a lot of taxes or big commission when you sell her to the next guy.
With all due respect to some of the well meaning posters above. Having taught perhaps 100 or more people to sail in my life, the traditional cruising boats suggested above would be just about the last boats that I would ever recommend for a first boat. Even if you had the budget to buy one in decent shape, (which you don't) I would suggest that you put boats like the Albin Vega 27, Folkboat 25, Contessa 26/ Taylor 26, Cape Dory 25D, Pacific Sea Craft 25, Pacific Seacraft's Dana 24
,Nor'Sea 27, the PSC Orion 27, and the PSC Flicka 20 put them all at the very bottom of the list for a first boat, or cross them out entirely. You might be able to learn to sail well on something like these but they are obscenely expensive cult boats that have such docile sailing capabilities that frankly would not be a great choice for a place to learn to sail. (and that from a guy who loves Folkboats). And whoever suggested a Pearson Vanguard; good grief man, what are you thinking?
So while it may be tempting to look for the perfect boat, or your long term love of your life, trying to buy your long term boat as beginner makes about as much sense as marrying the first girl you ever went out with after only one date. Think about it.....That's my story and I am sticking to it.