I'm going through this very process right now ..digitising my vinyl collection using my Linn Axis turntable. I ended up buying the Creative XFi HD USB external sound card which does 96KHz/24bit recording. Cost me about £60 (25% off current price) and is good quality. Can use it afterwards as a DAC, ADC, preamp and headphone amp for my laptop/hifi. Has headphone output, microphone input, optical digital input/output, analogue line input and most importantly a dedicated phono input for the turntable. The supplied recording software is very easy to use and I use it for editing and de-clicking the crackles and pops. You need the patience of a saint to digitise your vinyl .. it takes ages .. and you need to make sure your record and stylus are super clean .. you are effectively going to be creating a new digital master so you want to make sure there is no dust/static etc. to minimise surface noise. I normally play the album at least once to clear the grooves before recording it! The sound quality of the digital recording is very good .. just like playing the turntable but without the hassle! The files produced are quite large at 96K/24bit but worth it and the improvement over 44K/16bit is noticeable.
PS If you are serious about digitsing your vinyl and have a lot of it, it is worth investing in a new stylus for about £30 and an external ADC device like the ones mentioned above (Creative, Rega Fono, NAD PP3i etc.) or even one of the professional ADCs. Once you have finished you can sell on the equipment, or keep it as I intend to do with the Creative box as it is such a versatile quality bit of kit for the price. The normal microphone input on a PC/Laptop might not be good enough and suffer too much noise, and will not provide the right input impedance and equalisation for your turntable phono outputs.