Been there ...
I spent my first year living aboard my Excalibur 26. The boat had no pressure water system and no hot water. It had 55" of sitting headroom. I shared the boat with two dogs. I sailed and raced the boat, dogs and all. In '95 I got my Catalina 30. Compared to the Excalibur, it was a palace! Standing head room (I'm 6'1") and room to swing a cat. I lived on the boat for 5 years and loved every minute.There are some harsh realities about sailing oceans in small boats. little boats are slow. you would be doing well to make 100M a day. That means 27 days at sea to cross the Atlantic. Finding room to stow all your stuff, plus food and water for over a month at sea might turn it to a large headache on a little boat. If your wardrobe is a spare pair of jeans and 3 tee-shirts and you don't mind freeze dried meals, you might have enough room for water and fuel. Count on 27 days plus a 20% safety margin. Very few little boats have 65 gallons of water on board ... going to bring a friend? Now you need 130 gallons of water or a watermaker (neither option is cheap). All the stuff will not make your boat faster (Just the water in the tanks is over 1,000 pounds). Weather forecasting beyond 3-5 days is very unreliable. The small boat has to be a strong boat because it is more likely to get caught in bad weather.$15-25,000 boats are in no condition to cross oceans. $15,000 does not go very far when you are planning to go offshore. You won't be getting all new standing and running rigging for that price. The lifelines are probably PVC coated, yellow, and cracked ... they need to be new. Jacklines, safety harnesses, good foul weather gear ... I'm not talking fancy, just sensible. What condition will you find the engine and charging system? The boats in your price range are 25-35 years old, they are going to need work.A couple of years ago, a young woman was Given a 29 foot boat. He plan was to sail single-handed around the world. She talked a good game and got some corporate sponsorship. Over $100,000 was spent on the boat before she left ... she made it from Victoria to San Fransisco before she quit.Somewhere between $15 - $25,000 and $125,000 is a sane figure. Yes you could do it on $25,000, but you would have to have some pretty good luck.I wish you the best!