Chip:
I record some stuff from Youtube as well. Your issue might be that it hiccups during the Youtube playback due to bandwidth or buffering issues and has nothing to do with your recording or burning process.
It might help to wait until the song plays through once in Youtube before you start the recording process. Just hit replay in Youtube to play it again. The second playthrough may not have the hiccups.
I use Audacity and have not had any issues at all.
The procedure:
Open Audacity, hit the red button to start recording
Go back to Youtube and start the song playing
Let it play through, then hit the yellow button in Audacity to stop recording a couple of seconds after the song finishes.
Cut off the blank few seconds at the beginning of the recording and possibly at the end.
Alter the sound as desired using Audacity tools. I usually don't do this.
Export as mp3.
I then use the free "mp3 gain" program to normalize the volume level. It works ONLY on mp3 files.
If I later want to burn the song to CD, I convert back to WAV using Audacity and burn using a simple program called Imgburn--which can also burn any type of CD, not just music. The conversion back to WAV supposedly affects sound quality, but I have never been able to detect that by ear.
The consensus I have read regarding blank CDs is that "Taiyo Yuden" makes the best stuff. You can only rarely find them (rebranded) in retail stores, but they are very easy to buy on the Internet.
http://tinyurl.com/re3ar6
Above is a good source for Taiyo Yudens.