Probably safer than you are in anywhere in North America. Easier and cheaper than what? — a hotel you find on expedia? I’d go for hostels, you’re bound to meet people in the common areas and the dorms. I would book 1st night before I left home. I would try to book the rest via phone or internet a couple of days in advance. I would make a point of arriving in a new city by mid-afternoon if I didn’t already have a reservation. Arriving by mid-afternoon is probably a good idea anyway in winter. Europe is farther north than most American cities. While, for the most part it isn’t as cold as the northern 1/2 of the US, it does get dark earlier. Trying to find your hostel in a strange city is less daunting in full daylight.

For a trip this long I wouldn’t worry too much about scheduling, other than what you’ll have to do to deal with Schengen visa issues. If you’re American, you can only stay 90 days out of a 180 period in the Schengen zone without a special visa. Wikipedia has a pretty good article about Schengen.

(don’t know how to quote, but bear with me here)

I have traveled and lived in Europe for some time now and as a young woman traveling alone I find it helpful to really study maps before heading somewhere. Walking around with the map all folded out has sometimes drawn unpleasant attention. Not in the sense that I feel like I am in danger or anything, it just saves me a lot of annoying hassle. If there is one particular place you have to find, write direction on a small piece of paper (“this street” left, “that street” right and pretend that you know where you are heading. Google maps are great if you have internet access.

Hostels are the best places to hook up with travel companions and couch surfing is a great way to integrate with the locals.

As for planning I second oldlady and really suggest you just go with flow as much as possible; listen to other travelers, where they have been, what hostel was good etc. Even join them!

Beware that airline tickets are sometimes way cheaper than train tickets (ryanair f.ex.) and that you can save a penny or two buy staying at airports overnight before an early flight or take an overnight train (seats are less expensive than beds and not that uncomfortable)

France has a site called allostop.net where they hook up drivers and hitchhikers safely and you pay a small fee to the driver.

… and last, but not least I would make a point of booking well in advance concerning holidays (like New Years), but that you probably already imagined