Rob, they easiest way to do it would be to 'rip' the tracks you want off the discs, save them all to your hard drive and then burn the CD-R when ready to do so.
Pop in one of the CDs and within Easy CD and select which track numbers you want. It's been a while since I've used Easy CD, but I think it's just a case of clicking on the tracks, doing a right-click and selecting "Extract to Wav" or something similar. Save the files you want on the hard drive.
When you've done that for all the songs you want, create a new audio CD layout in Easy CD and just add the .wav files to it before burning.
Ripping to WAV format wont lose you any quality. WAV files are uncompressed (and big!). It's possible that 'ripping' may introduce errors and glitches if the hardware isn't set up or working properly, but that would probably also affect direct disc-to-disc copying anyway. It probably wont.
CD tracks aren't wav, they're in a different, CD specific format.
Easy CD will be perfectly fine for most of your work. Nero is certainly more accurate, but this only really shows itself when you have 'problem' discs. For example, a CD that EasyCD refused to extract from sailed through Nero with no problem.
Since you've already got it, use EasyCD for now and look at changing if you have problems.