If you finally go for the carpet, I'd suggest that you install a good floor matting system underneath, (preferably a plastic one) that will keep water and vapors from soaking your carpet or it will also rot, but before it rots or get visibly moldy, it will smell... badly.
(I tell you that from personal experience.)
There are though, some options that you might want to consider. Some companies offer flooring options that are specifically developed for basements.
If you search specifically for it over the internet you will find plenty. Some of them will even give you the look and warmth you are looking for, and none of the hassle in the long run.