How many records are we talking about here? Keep in mind that any transfer will involve real time playback, so its anything but quick. Priority should be given to music that has never been released to CD. Here is what I use for vinyl to CD transfers. Note that this is for modern microgrove 33 1/3 and 45rpm records, not older 78rpm records.
Turntable: Technics SL-1300 Direct Drive. These turn up on ebay ALOT and are built like tanks. Any Technics direct drive model is fine for this job, later models have a quartz speed lock for accurate playback. I have it hooked into a standard stereo receiver with phono preamp and run it into a decent soundcard.
Another option is the Audio-Technica LP120 and LP240 turntables, which are basically an inspired copy of the classic Technics turntables. It has direct USB output, some folks aren't a fan of its built in pre-amp however. The stylus it comes with isn't the greatest either (ironic given the manufacturer). If you find a Technics direct drive turntable for less then the LP120, pick it up. Just because the LP120 looks like a Technics, doesn't mean its as good as one. Avoid the ION, its junk.
Stylus: This is likely more important then the turntable. I have an Audio Technica AT331LP linear contact stylus, which is sadly discontinued. A suitable replacement is the AT440MLa, but it can be pricey. If anything, stick with an elliptical diamond stylus or try hunting on ebay for an older Audio Technica "Shibata" stylus.
Soundcard: I used a Soundblaster AWE64 Gold, because it was the best I had at the time. A used Soundblaster Live! PCI card off ebay will produce decent recording as it has low noise levels and a decent digitizer. You don't have to worry about this if you use the USB turntable, but who knows how good the digitizer is in them.
Post Processing and Restoration Software: Diamond Cut Audio Restoration Tools (also konwn as DCart, get it at
http://www.diamondcut.com ). This software was developed specifically to restore early phonograph recordings and has a ton of tweakable filters. As an added bonus, it can be used to restore audio tracks on video recordings as well. The manual alone is worth the purchase price and includes many how-tos for restoring audio. When recording, just record an entire side of an album at once. You can add track breaks later in post processing.
Also important is cleaning your records. Dust = noise. The Nitty Gritty cleaner is popular if you are serious, otherwise look online for various ways to clean vinyl without damaging it.
Is the setup I use audiophile grade? Heck no, but it sounds better then most setups with a cheap conical stylus and belt driven turntable. Most popular recordings aren't the best quality pressings to begin with and wouldn't benefit. Plus the law of diminishing returns kicks in... you got to spend a lot for what amounts to a minimal increases in quality.