Rega make very good turntables and great tonearms - had a P3 with the RB 300, and the sound was very good indeed.
More to the point, just bought a Debut III with cartridge and phono stage at the local sales, so will give it a spin on the weekend and report back. My initial feeling is that the cartridge is the weak link, but luckily I have a decent Grado on hand. Asked about the Project on this forum and got a very positive response, so I'm hoping to be pleasantly surprised.
But bear in mind I bought the Debut because it was cheap (100?) and I don't have many LPs. If you are serious about getting into vinyl, then don't muck about and go for the P2 or better. There's far more variation in sound quality from turntables than any other component, and sadly it does tend to be related to price. A cheap turntable sounds just that, and a better cartridge (you'll end up going down that route, believe me) only highlights the deficiencies.