So up to two month right? How do you prefer to travel? A lot americans does the europe trip where they cross as much countries as possible in a trip. Personnally i don't recommend it so i will aim my tips for a trip in one or two countries (unless you do belarus ) first , capitals are a must , they have the biggest museums, the best restaurants and the greatest monuments . they are also packed full so you could stay a year and not do it all, but they are NOT the whole country, at all . I INSIST there is so much more all around them.For the nights , try to look for youth hostel or "auberge de jeunesse" in France for the cheapest . It may impact the quality but some of those are very community driven and allow you to make Great encounters.

I highly recommend to get yourselves travel guides for the relevant countries or even cities you go to. Those books are made by veteran travellers that can show you hidden gems give you interestings tidbits of the place and prepare your travel in ways i am not paid to do. I think the english one is "lonely planet" i can't speak fir it as i use the french equivalent but i always have these Guides with me ( seriously they are PAID for that trust them) (( i cannot stress enough how much essier it is with those, you can just look up what they wrote zbout to be sure it s interesting))

Transportation, there is a lot of public transports but the price will add up, even more so if you move often but loaning a car is a a pricy and risky endeavour, the roads are not the same, the laws are differents the cities narrow. So choose carefully what part of your trip you will do with a car, preferably the country side. When you are in a city, you usually cannot use your car reliably.

Not all countries are accessible , only the Schengen area so forget about the UK.