Hola and Welcome sportslover,
For starters, only 14 days and 7 countrys will be hectic to say the least. I think you should do at the most 4. I would look at the list and decide what ones you really want to see. If you tried to do more then 4 countrys you will have a hard time really enjoying the time you have in each place.
As for the Eurorail pass vs. Ryan Air or Easy Jet that is really up to you. When you make your list of countrys and they are close to one another I would say use the Eurorail (FYI - The Eurorail does NOT work in England, you will need a Britrail pass)
If the countrys are a good distance from one another I would use EasyJet or RyanAir, however, keep in mind that the airports sometimes are a good ways out of the center of town (thats really the only con to air travel)
As for cost its totaly up to you.. If you wanna do it as cheep as possiable you could stay in larger doorm rooms, eat mainly bread and cheese, and not party (drink and such) too much. I would decide how much you want to spend a day. For example I will plan on spending 80 Euros (around 100 USD) a day. This is my breakdown:
25 Euros a day for Room
25 Euros a day for Food
30 Euros a day for Partying and Such
You also have to factor in things like taking the night trains will save you money on not having to get a room. I won't be partying EVERY night so I will save there too.
Flying in from the US you have 2 good options for good fairs. Flying into Brussels or Amsterdam are the cheepest places to fly into. I would check a site like travelocity and use the flexable dates option to see when I can get a good cheep flight.
Hope this helps