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Boats are hardly insulated at all, they're for warm weather usually, unless you're spending a lot more than $3k.
You'll be cold, sick of constantly rocking back and forth, tires of not being able to stand up, and sick of walking across the dock to the marina at 3am when you need to use the bathroom.
Or just use the bathroom on the boat and pay someone once a week to pump it out. That's not cheap either depending on where you are.
Sounds like a shit idea OP.
A houseboat would be a waaaaayyyyyyyyy more practical idea. They're basicslly a floating camper.
A small sailboat is meant to sail, the living quarters are secondary. They are just big enough to sleep in and sit in, that's it. 50 sq ft if you're lucky with 5 ft ceilings.