how long do you suspect it will take to travel from London, Paris, Amsterdam, Berlin, & Budapest if i only care to spend 1-2 days @ each destination. (with the eurostar and eurorail pass) and do I have it in the correct order if my starting point is London? Thanks for any help!
You might want to check the German Rail Website to get some ideas on the travel times to each of your destinations.
The time from London to Paris (via the EuroStar) is about 2.5 hours (I can't recall the exact time). You'll be travelling from London St. Pancras to Gare du Nord, so there will be a bit of extra time to get to and from each of those stations to your Hotel.
Paris to Amsterdam is an easy and fairly quick trip. Amsterdam to Berlin is somewhat longer (~7 hours), and not sure about Berlin to Budapest.
I'm assuming you're using open-jaw flights, inbound London and outbound Budapest?