If you simply must rent a car, check with the airline for tie-in discounts, or call around to rental agencies to find any package or leasing options. Keep in mind that Europe is expensive and renting a car will really chew into your budget. Fuel can be three times the price as home.

A rental car offers the advantage of immediate mobility. That's about the only advantage I can think of. It is expensive, foreign road rules can be hazardous, and all in all it is an impediment to integrating into the local culture. Still, if there are four or more of you it might be cheaper than other options.

Flying around within Europe is really not a feasible option. For the distance they cover, flights in Europe are ridiculously expensive. If you must fly to save time, you are probably in too much of a hurry. The one exception is Sweden, where the local airlines used to offer a deeply discounted student standy fare within the country. Check once there to see if it's available.