How much money would it take to travel to all these places?

That would depend on a lot of factors. Where you are willing to stay, what you plan on eating, whether or not you will have extra time on your hands in which case you could volunteer at some places in exchange for food or room and board, more money if you plan on getting souvenirs, etc. You will have to research these places individually to try to figure out about how much you will need for each seeing as some places will be more expensive than others. If you have friends throughout the US (or wherever) who would let you stay at their house, that is a good way to travel on a budget. I would also imagine buying tickets in advance and/or signing up for travel websites newsletters could help you get a better deal. I can tell you for sure that Sweden is very expensive and I'm pretty sure many other European countries are as well, so save save save. Greece isn't Expensive, also isn't cheap. It's an inbetweener, but right now their economy is actually down so now could be the best time to travel. You would have to plan out an entire itinerary to see where to start, where to stay, how to get from point A to point B, and everything inbetween before it's all over. Good luck.