Sorry, as you should have realised from the note on the player, the older clips are deliberately low quality. This is so that they will play for everybody visiting the site - not just people looking at it when they're supposed to be working - even if you've connected using an ordinary modem and phone line you should be able to hear the music (albeit rather tinnily).
More recent ones are a better approximation of what the music really sounds like.
I could put some high quality clips up too, but they take too much space so they'd either have to be really short or I'd have to rent lots more space. I chose instead to put long clips at low quality which gives you a better idea of both the various records used in a set and how they get mixed together.
If you can hear the music, but it keeps stopping and starting, then I'm afraid that either your connection really is too slow to support listening to music at all, or there's too much going on for your PC to keep up with. Try closing some applications and see if that helps.
If you don't get a set of controls that look a bit like a CD player with play and pause buttons, then you don't have RealPlayer or RealOne installed. This is a bit of software that you need to have so you can listen to them. Visit www.real.com to download it for free. Note that some versions of these players are Adware - software that's free to you to use because it advertises things to you, and may even monitor your surfing habits and collate the info (nothing more sinister than marketing purposes, though). If you don't like the idea, read the licence conditions before loading to make sure you want what you're installing. I'm hope to upload some mp3 format files for you to try instead (but they seem a bit big!).
If you've got some other problem, drop me a mail to describing it and I'll try to help.