What you will need is a sail boat. I would think about moving close to the coast where you could meet people who would be willing to show you how it's done. Finding a trawler capable of going places you want to go, with the budget you have set, is going to be really tough to do. But lot's of people do it in sail boats. There are lot's of videos on YouTube of people doing what you want to do, but 99% are doing in sail boats.
Check out these channels:
http://www.youtube.com/channel/UCgAW5P0Xf4iOBAr4PSQ9oRQ
http://www.youtube.com/channel/UCRqsOR0Y2zru-jXSzLcMcxg
http://www.youtube.com/channel/UCkYfFeySHGN4DPrOc9So7PA