If you want to minimise the fuss, you could go with a tour group, which you could then see the a couple of countries, but you'd compromise on things like time spent at attractions, etc.
But if you want to do your own stuff, I have to concur with alot of the other posters in the forum. 14-18 days is really quite short to see 4 countries. Travelling between the countries will take up time and you'll need to factor in contingencies like navigating the language barriers, weather/seasonal changes, public holidays (some places don't open), or if your train came late and derailed your plans (pun intended) to reach a certain place by a certain time (which happened to me). I would suggest that 14 days is probably ideal for 5-6, at most 7 cities, and it depends on where you want to go, what sort of sights you want to see, etc. You can also base yourself in certain cities and do day-trips to other smaller cities from there.
There are a lot of good travel forums out there that would give you advice on how to go about planning your trip - and they've helped me plan my first trip to Europe (3 weeks, to Munich and parts of the former Yugoslavia). A good start is to identify which cities you really want to see, and try to pick those that are closest to one another, dropping others to the next trip. Those are my 2c worth of travel planning for Europe. Hope it helps.