Use EAC (Exact Audio Copy) to snag the files from the CD and store them on the USB drive. If you have an Oppo 983 or similar DVD player, just pop the USB stick into it and play away...
Depending on how many CDs you want to copy, a USB flash drive may not get
you where you want. The largest one I know is 32GB, which is quite large, but
depending on where you are, it may be difficult to get a 32GB drive for a bit. A
16GB drive doesn't hold many CDs when the data is not compressed.
As to how to put the music on there... If you were using iTunes on your
Windows PC, you could simply point the iTunes software to that USB flash drive
(when it is plugged in), and store your music there when you rip it, and then
your iTunes would get the data from there when playing music. OTOH, I think
you would have to have that drive plugged in every time you wanted to rip
music, add it to your Library, change your Library, etc, which may eliminate any
usefulness of it being portable.
4GB is a small hard drive. Music, when uncompressed (to retain quality), takes up a lot of space. Nero would probably work, but there are many other players too. The archives here and over at the PC Audio section of Audioasylum.com are priceless resources so I highly recommend anyone starting on a particular path to avail themselves of the archives.
As T_Bone says, 4GB is a pretty small drive to consider. Even if you use one of the lossless compression formats like FLAC or Apple Lossless you'll be able to put only 150-200 songs of typical length on the drive. Using mp3 compression will multiply that number considerably while giving away some audio quality. That might not be a consideration, though, depending on the rest of the playback system and your ears.