1) Nothing wrong with single handing a world cruise. I do recommend picking up crew or having family join you at times. Let others share in your experience, even if only for a week or two. A crew person, familiar with the area you are in, will add greatly to your cruise.
2) The best size and type is what fits your personal requirements. Stephen list 27 to 30 feet. In a monohull I'd choose 35 feet to 45 feet, I think the minimum size certified for offshore is 35 feet (insurance), not sure though. You can single hand any boat if it's setup properly and no more difficult to sail a 45 footer then a 27 footer if it's rigged properly. A bigger boat means better accomodations and safety.
3) Absolutely go east-west if you have a the ability to choose. It's the prevailing wind patterns for the best latitudes. West-east means high latitutdes, bad weather and few places to stop, all cold.
4) I could fill a hundred pages of great places to see, the next person would list another hundred. Start with Cornells "World Cruising Routes". Pick a basic route; you don't have to keep to it but for planning its a good place to start. Then get guidebooks, or research on the web, for countries along the first part of the journey. You can do the whole route but it will probably change anyway so keep it to the first year of travel. Lonely Planet has excellent land based guides but still good info for the yachtie. The real yactie guide books you can buy once you have firmed up the route and are ready to set off.
5) Keep away places. Certain areas and countries...just common sense here. For places to stay away from, in individual countries, you'll know this from other yachts and the marine nets in the area. Even natives will tell you who not to deal with or unsafe places to go.
6) Go do it! Don't just dream it, make it happen. It's too easy to fall into the comfort of the marina...leave the pier and make the journey happen.