Usually what I do for max speed is:
-Reboot your computer
-Close all chatting programs (mIRC, X-Chat, Trillian, MSN, etc.) or internet browsers if you have them set to start up with windows.
-Disable your anti-viruses
-If possible, disable softwares that search for updates automatically on a regular basis
-Afterward open Audacity, then ePSXe, but don't start MTVMG/Music2000 right away.
-Set up your windows so you can see both softwares windows at once. This is important cuz if you switch between them after doing the following by clicking on the taskbar buttons it will freeze literally for like 2 minutes.
-Now Set up both softwares to high priority.
-Start ePSXe emulation, go to your song and all.
-Now go back to audacity by clicking on the window and start recording.
-IMPORTANT! You must minimize Audacity window, because just the track graphic showing up on Audacity takes precious ressources. Hiding it will improve performance.
-Now click on ePSXe window and start playing your song. Don't close the window, keep focus on it and do nothing else. Altough it worked for me almost all the times sometimes I still needed a few tries until I get absolutely no skipping at all. But it worked pretty well in overall. Keep in mind I have a 2.93 GHz computer (not dual/quad core though) with 1 GB RAM.
-Now when you finished, press Esc in epsxe, then stop recording in audacity.
I hope this works for you. Else I am afraid you may need a better PC