Well, the Linn Sondek LP12 might come with the original Linn arm and cartridge. My dad uses a Thorens deck which is a TD-126 Mark III fitted with an SME arm. If you see one of these cheap, I'd go for it. Perhaps the easiest thing to do would be to buy one of the Pro-Ject turntables that AudioArcher recommended. I did see a Pro-Ject turntable reviewed in What Hi-Fi? and it was meant to be very good. I certainly am no expert on turntables and if you were to buy one second hand, it would probably be better if you had experience with turntables. You could buy a second hand one with a bad stylus or have the wrong combination of arm/turntable/stylus etc.
I don't think you loose that much buying a cheaper turntable. Even though it's a transducer, I'd probably be hard-pressed to tell the difference between my dad's Thorens and one of my cheaper Technics turntables. If you do go for one of the Technics DD turntables, check to see that you can activate the motor with the lid up, otherwise you'll have to wipe the disc with a suitable cloth.