If you want to do compilation CDs with your own music mix, that isn't hard. First, as suggested above, use Exact Audio Copy to rip the original CD material to your hard drive in either WAV or FLAC (lossless) format.
Then, burn your selected songs to a quality CDR. I use Taiyo Yuden blanks which is an excellent, consistent brand that makes their own CDRs. (Some of the popular name brands are made by the "factory of the month club" so you are not getting consistent quality.) Mitsui is another good brand.
Also, it is typically best to not burn a CDR at the fastest speed. I typically use 16X. Interestingly, the slowest speed your drive can write at is not necessarily the highest quality. You may want to invest a bit of effort and "waste" a few CDRs. Burn the same thing at several speeds and then re-extract them using EAC. Settle on the write speed that gives you the fastest EAC extraction with the fewest errors.
There are some golden ears who will have more complex rituals and rules than noted above (using black or gold CDRs, etc.) but the above more than sufficient for my needs.
