First rule of backpacks from my experience is find the smallest backpack that you think you'll need and then get the next smaller one. Unless you're gonna be doing a lot of souvenir shopping, you don't need much space if you pack right. I dunno what you'll be using the pack for when you come back home, but that might help decide the size of pack you have.
Rick Steves sells a cheap, no thrills backpack that's small enough to carry on the airplane. It costs something like $75 if you get the railpass on his website ricksteves.com
I have a terribly bad back and ended up with a really nice EagleCreek for my 3 month trek. It was much bigger than I needed. I can't remember how big it was but its the one that sells for about $169. I was just looking on their website and found this
http://eaglecreek.com/10041.html If I had it to do over again, I'd get this one cuz it has a daypack(vital, trust me), compression straps, nice looking straps, and it fits the carry on requirements (14x22x9)
Never get an externat frame!! And one of the other reasons I'd like to have had a smaller pack is sheer ease of getting around. Getting on a packed subway or up a tight fitting flight of stairs w/ a big pack sucks, trust me.
There is always somewhere to put your pack in hostels, even if it's just locking it to your bed. That being said, buy a couple of locks for your zippers and one cable type in case you have to chain your pack to a bed in a hostel or on a train.
In terms of the train question, you need to at least get an idea of the which and how many countries you want to visit. I spent 3 weeks each in Spain and Italy and didn't get to see all I wanted to, so plan on going back to Europe sometime in your life and enjoy 2 or 3 countries slowly. Give yourself an opportunity to get to know the lay of the land before you take off somewhere else. If you decide more specifically where you want to go, let me know and I'll help you with specifics like train passes and stuff like that.
Good luck and have fun....I miss how much fun I had planning my trip
Jason