$30-50 can get you a fairly decent boat in the 30' range and still leave you enough to have some budget for re-fitting, upgrading and customizing it.
I'd also have to ask what kind of sailing you'd want to do with the boat? If you aren't going to be sailing the boat, buy an old poweboat, which will have much more living space than any sailboat you could afford.
Your best bet for a liveaboard slip is probably Constitution Marina, which has a long history and tradition of liveaboard sailors. They're not the least expensive, but unlike many other Boston area marinas, they're open year round.
As for boats, there are plenty of boats in the 30' range that might work for you. Few of the boats in the 30' range have a built-in shower, and fewer still have a separate shower compartment. Given your budget, you'll be looking at older boats... I'd recommend looking at boats in the $30-35k range, pricewise, and you'll probably be able to purchase them for a bit less than asking price.
I'd recommend you read the Boat Inspection Trip Tips
thread I started, as it will help you determine whether any boats you look at are even worth going forward on, saving you the price of a survey on boats that aren't worth looking at further.
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You know what the first rule of sailing is? ...Love. You can learn all the math in the 'verse, but you take
a boat to the sea you don't love, she'll shake you off just as sure as the turning of the worlds. Love keeps
her going when she oughta fall down, tells you she's hurting 'fore she keens. Makes her a home.
—Cpt. Mal Reynolds, Serenity (edited)
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Still—DON'T READ THAT POST AGAIN.