How do I make "greatest hits" w/out CDRW changer

[stemata]

I very recently purchased a CD-RW drive (Sony CRX175M). I thought (wrongly) that I could use my CD-ROM to make my own "greatest hits" from various audio CDs. I wasted several CD-RW discs before I learned anything about "multisession," and the fact that CD players don't read in multisession. In other words, I burned one song from a disc, and then found out that I couldn't continue to burn additional songs onto the same disc. How can I do this without a CD-RW changer? Is there some way that I can copy the songs onto my hard drive (such as in MP3 format), and then burn the songs all at once onto the CD-RW disc? Any other suggestions will be helpful. Thanks for your help!