You need an ocean worthy cruiser. BUT... by asking the question, you sound like you don't know how to sail.
If this is really an interest, and you want an adventure -- I'd recommend crewing at yacht-club races.
I knew someone who raced and I'd crew on his boat one evening a week for a couple months -- and it was VERY fun.
It helps to know someone at a yacht-club to race with -- but you could just show up and tell the race organizer you'd like to crew. Someone is usually short a man -- and would likely be happy to take you. It would help if you took a sailing course -- maybe at a community college. I took one and it was affordable at ~$75 or so for a few class sessions and 3 or 4 sessions on the water.
Once you think you could spend a long time on a boat -- a couple things you could do:
1) There's a 2 week race every year -- i think in July -- from California to Hawaii. Not sure who the organizer is, but I'm sure you could google it.
2) Travel to Greece and rent a cruiser and sail around the greek isles. I'm quite certain you'd need to be certified before anyone let you get on a boat .
I've never done either, but I've read stories and they both sound like a great adventure.
I don't think I'd be crazy enough to try sailing across the ocean. I've been on inland waters with very strong winds -- and it was a bit scary. I couldn't imagine 30ft swells, pouring rain, and no-one in sight.
If you've gotten this far and are still interested, I'd recommend doing a LOT of research.
edit: Minimum to single-hand -- probably a Flicka 20'. They aren't cheap. Also remember that sailing is only 1 part. There's navigation, too. Plus planning for nutrition, first-aid, etc. Basically, this shouldn't be something you jump in to. It should take a LOT of time to prepare for such a thing.