I have lived aboard my 30' motor vessel for about 3 years in a marina north of Seattle. I traveled all throughout the puget sound and San Juan Islands, but motoring is very expensive. It cost me over $500 to go 150 nautical miles one weekend. As far as just living aboard in the marina, my cost was about $300 per month including electric, water, garbage, showers, and laundry. My boat was paid for, but I did have to keep it insured to be moored at the marina and that cost me about $400 per year.
You could have a houseboat in a setting like I was in, but you have to remember they are not as sea worthy by design. Yes, houseboats do have motors too. Some are inboard engines and some are outboards. I don't think I have ever seen one without a motor unless it was trashed or home-built.
If you truly want to travel around the world, you will have to have a sailboat unless you are just crazy loaded with money for fuel. I would not want to take to open seas in anything smaller than a 35' boat. It should have a diesel inboard engine for motoring in harbors or when otherwise necessary. Solar panels are reasonable now and are a great idea to have on long voyages. Some boaters even use marine wind mills to generate electricity, but that is more expensive.
You should have water purifier onboard that can make sea water drinkable, gps, compass, navigational charts, vhf radios, a satellite phone would be ideal, plenty of food that is non perishable and protected against water penetration. Always file a float plan and make sure that everyone knows when you are supposed to arrive at your next destination and what route you were taking to get there. Check in often. Remember to keep informed on weather conditions and avoid severe storms at sea at all costs as even the most seasoned of sailors have lost their lives in rough seas. You can stay relatively close to land on most of your voyages around the world, unless you decide to head out to Hawaii or other remote islands.
I would keep serious weapons onboard for a world voyage as pirates are a very real thing and they don't just make you walk the plank. They cut your throats, rape your women and children, and take anything of value before sinking you and what is left of your boat. Do not let a boat approach you that is not a police or military boat and in some parts of the world they might even be worse. Warn the vessel on the vhf radio to stand clear, announce the same over the loud speaker, and even fire a warning shot over their bow if you feel they are a serious threat. Its best to steer clear of other boats that are suspiciously far out in desolate areas. I would keep some cash, travelers checks, and possible gold coins with you for supplies, etc., but I would keep most of my cash in a bank that has debit card access. This won't help on a remote island in the south pacific, but in most other countries, the debit machines will automatically convert your currency to their currency when used as debit or as visa logo'd card.
Take lots of sun block!
Years of boating and thoughts of heading out around the world one day myself.