The advice given above is correct. Your US green card doesn't mean anything regarding your ability to enter other countries (it is important, of course, for returning to the USA). I'm a US citizen so I travel on a US passport. My wife is a green card holder, but travels on another country's passport. While I can often (usually) enter many countries without any visa, she often has to jump through the hoops of obtaining a visa before we leave. Frankly, it's a pain (so we're working on her naturalization before we attempt another trip).
Bottom line: what counts is the country whose passport you use. Your green card is only useful for (re-)entering the USA.
As stated above, you will need a visa to enter the UK (good luck - that one is expensive, a major hassle, and involves providing plenty of annoying biometric data, e.g. fingerprints). You will need a separate "schengen" visa for France/Italy/Holland (one combined visa for all the schengen countries). That's a fairly straightforward process, but can be a bit complicated since the schengen countries all seem to want to "pass the buck" (American expression meaning give the responsibility to someone else): you need to apply for the schengen visa to the country where you will be spending most of your time. If your time will be split evenly between multiple countries, they want to to apply for the country you will first enter. Don't know about Switzerland.
Good luck, get things started as soon as possible (it can take a while) and have fun!