Best way to copy LPs to CD's using a Computer


Please help! I want to transfer many of my lp's to digital and onto CDs. What software programs have you used that you could recommend and what would you suggest as the best way to connect from the integrated amp to the computer to transfer the signal?
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I have been trying to find a high fidelity way to do this for years, but i've never found a well documented example.

There is much more than just the software choice. What is more important is the hardware.

Hardware wise - How can we get our LP music to the computer with the absolute most minimum comprimise? Spdif clearly is not an option for high fidelity, there must be some better way.
I second RW's response. Four or five years ago I purchased a stand-alone component, Pioneer PDRW-8339, for several hundred dollars. I have not been disspointed. The unit has made hundreds and hundreds of CD's with audio quality very close to the vinyl source itself. I think that this particular unit may be discontinued, but I have seen them used on ebay for around $150. I am sure there are other similar brands that will also give you good results.
I have digitized hundreds of LPs with an iMic and the free software Final Vinyl. I have had excellent results. I have an Apple G5 and I'm not sure if the iMic/Final Vinyl is PC compatible.
Oregon - you said it! I enjoyed copying my vinyl to CD, as I was listening to new music and getting exposed to it. Make it part of the listening experience!

Goatwuss - I think the best way to make truly hifi reproductions is with an external, USB analog=>digital converter, like the Apogee.