London – Amsterdam, either EasyJet or train, the man in seat sixty-one has a good page with all options: http://www.seat61.com/Netherlands.htm#other%20destinations%20in%20the%20Netherlands
Amsterdam to France or Germany, it does make sense to use a train pass there, otherwise, a long distance ticket with a via. (like Amsterdam-Paris-Munich or Amsterdam-Cologne-Paris-Nice or something like that.
The German rail planner is a good one for travels like that:
http://www.bahn.de/international/view/en/index.shtml
Seat 61 has info on passes compared to individual tickets too.
Starting page for the site: http://www.seat61.com/

Germany or France to Greece or Spain, flights.
Greece to Italy, flight or ferry (pass gives reduction on the ferry). Greece to Spain flight, Spain to Italy, or vise versa, flight, but there is an overnight train too, so if you have a pass, you can use it there.
For flights check one of the search engines just for those:
http://www.skyscanner.net/
http://www.whichbudget.com/

For accommodations in Western Europe you will need more than $ 25, I am not sure about southern Europe, but the dollar is worth much less than the Euro, so better bring as much as you can.
If you are younger than 26 you can count on about $ US 50 minimum per day, plus your long distance travel cost, if you are older it gets much harder to travel for that budget and you should count on $ 75 minimum.
That is absolute minimum, if you want to eat out, drink, spend on sightseeing and so on you will likely spend more.

Also read in the other questions here, as this is a question that comes around often and several of us answer many, each with our own preferences and knowledge.