As Marty said, iTunes/Win will convert non-protected files, so that is an easy option if available. Converting these files before moving them seems to be the way to go.
I have heard of no problems caused by either EasyWMA or Flip4Mac. There maybe files that these two programs stumble over, but that is usually because of corrupted files, copy protection, or DRM, and not the programs themselves.
I have seen very few 3rd party programs that actually cause problems in OS X or with other programs. I have installed many so that I can explore and test them and I have many that I use on a daily basis. Two good places to find out what is available for OS X are
VersionTracker and
Macupdate. Both allow user reviews and ratings and often the user reviews are bitterly honest. In comparing the OS X side of VersionTracker with the Windows side, I also find that the Mac community is more interested in making reviews and giving ratings.
Although these discussion forums were specifically formed around Apple's products, if you do find you are having problems non-Apple programs, you can usually get help in a related forum (such as help with WMP or Flip4Mac here, for example).
How to transfer the files? The easiest would be if you could network the computers together and then just copy from one to the other. If you have an external hard drive you could use that as a means of transfer (as well as the all essential means of backup). Then comes copying the files onto dvd or a cd and moving them over that way (these would also serve as a backup for you).
I would let iTunes do all of the housekeeping involved with setting up directories and folders. There will be fewer problems and you will have less work. Just drag the music files or folders onto itunes and they will be copied over into the iTunes music folder. You can use iTunes itself to manage your music library and there will be few times (if any) you will actually need to go into the music directories themselves.
As far as step-by-step instructions, let us know what you have done and what you are about to do or what you would like to do (what stage you are at) so someone can be more specific in advising you what to do.