Requires a really good A-D convertor. I would strongly recommend one built for this purpose. Should include a phono pre-amp.
Look at the Burmester 100. I will do precisely what you are looking for. Pricey... but they do come up used from time to time. VERY GOOD.
Works very well. The other limiting factor is the quality of your Table - Arm - Cartridge.
Any good ADC needs a really good phono pre in my opinion.