I'm a beginner in RE. So i don't know which environments are better for me ( Linux or Window , 32bit or 64bit ).
Which free tools are the best for each OS .Ollydbg is for Windows 32bit right?
There isn't really a "better environment" or "best tools", its all up to the RE tasks you are up against.
Since you said you are a beginner and from reading between the lines without a pre determined task, I would recommend 32bit machine and Ollydbg focusing on solving some CrackMe challenges.
You can find some of them here: Tuts4You - CrackMe