You always dreamed about globetrotting and going once around the whole globe? That is an awesome idea! At the beginning it feels like a crazy idea and even a big scary, but I promise, it is the best idea you ever had ;) Maybe you think about a specific country where you always wanted to go but was just too far away or you want to experience a lifestyle then a trip around the world is your chance! Depending on your budget, you can do backpacking, flashpacking or even luxury traveling. It is a good idea to get some impressions of destinations in magazines or guide books.
This is very difficult to say.. you can go around the world in probably 10 days, spending all your time on the plane and not really seeing anything. The time you need depends very much on the number of continents you want to visit, for example we plan to visit 2 continents in 5 months and it feels like quite a short time. So if you can only get off work for 3 months I would suggest you to set priorities instead of squeezing in everything. I think a good reference value would be about one month per country.. feel free to share your experience in the comments :) Below, you see one of the "standard" routes, which is probably also the cheapest.. you can get it for under 1500€. It is also kind of the highway of RTW trips.. you just see the most popular tourist spots, but you can use the time between flights to explore some more random places.. there are some questions you should consider to get started:
Check the climate for each country you plan to go and compare which directions suits you better... choose if you only want to have summer on your trip or get great deals in low seasons to save money, some countries are worth visiting the whole year round!
There is no best, they are all great! Some are easier to organize and cheaper than others. Also check my article about flight tickets to get an idea what is possible. In general you can say everything on the northern hemisphere is "easier" because most flight connections start or depart here.. crossing the pacific from Oceania to South America is only possible with two airlines and is therefore quite expensive.. same thing for connections from South America to Africa. Anyway it is an option and we are doing it ;) Our trip in detail you can find here.
Especially one route around the world is a classical also sometimes called the "highway", starting in Europe to South East Asia then Australia and from there crossing the pacific with a stop in Hawaii to Los Angeles, then back home to Europe. Of course if you not from Europe you start/end point is different but the route could be the same. This is particularly interesting for low budget travelers because this route you can get quite "cheap".
Don't forget to include several surface sectors where you travel with bus, train or car. You will experience the real life in this country a lot better. For example, arrive in Cairns, Australia and book your onward flight from Melbourne, with some weeks in between to make the route on your own. Most tickets offer option like this.