so I would like to start saving up for a trip I want to do, but I don't know exactly where yet. This is where you macrumors come in, where would be the best place to backpack across and want to gain lots of knowledge and experience the rest of the world. I was thinking south america or europe. Also I would like to know how much I would need to save up for a trip like this. I would like to go for atleast 3 weeks.
I would recommend Europe, its a beautiful place and there are tons of great museums, sites, food, etc. I am sure South America would be fun as well though, thats one of the next places on my list.
Europe has an excellent train system, the Eurail, which will take you pretty much any where you'd like to go. If you plan on going to a lot of countries it may be worth getting one of the many passes they offer. A 21 day pass is about $600, but there are many other options. Here is their website, check it out:
http://www.eurail.com . There is a map and such for route planning and all.
My suggestion is just to come up with a list of a few cities and how long you would like to visit each. Wikipedia is a good free source to find a few major things you might like to see in each city. Then you can plan your route and make sure you purchase the proper Eurail pass.
I don't usually stay in Hostels, but it is a good cheap way to stay. I'm sure some other members will have suggestions for websites to find a good Hostel, just looking, Hostels.com seems decent, but I've never used it.
From my personal experience, these are the places I would really love to go again: London, Paris, Venice, Florence, Prague, and Budapest, but there are many other great places as well. I'd really recommend Prague and Budapest, they don't use the Euro right now and the exchange rate for U.S. dollars is quite good, so these cities will be cheaper than London and Paris (London and Paris are more expensive even without the different currency). Italy is my favorite country out of all the ones I've travelled to in Europe and I definitely recommend it for a first trip. Rome, Florence, Venice, Cinque Terre would all be excellent places to visit. Rome, Florence, and Venice especially offer a ton to see, you'll be overwhelmed.
I usually spend about $3500 on a two week trip, you might be able to keep it lower, but I budget about $1700 a week (again, I stay in hotels and eat/drink pretty well when I'm there). I'm sure you could do it for less, but it's definitely better to have more than to come up short.