Hardware: get a decent card. I have a TV Wonder VE and its sound and picture clarity aren't very good. Record to something like a high bitrate WMV or XviD video.
Just use Movie Maker to edit the video if you don't need anything fancy. It's good enough for most applications, and honestly it's the best free video editor I've come across. It can put music behind the videos.
Photo Story can make some nice looking, documentary-style picture slideshows.
Digitizing records is pretty easy. You need to hook your turntable up to the line in (usually blue) port on the back of the PC, through a preamp. Make sure the turntable and preamp are grounded at least to each other, or you will get nasty 60-cycle hum in the recordings. Use a fine brush or some compressed air to get as much dust off the records as possible; this will make cleaning the audio up much easier.
Record using
Audacity. Make sure you tell it where to find the LAME .dll or else you won't be able to export to MP3. (There's guides on their website.)
Cleaning up noise is easy. Make sure you record some of the 'silence' between tracks. (I like using either the first few seconds along the outer rim of the album, or the wide parking groove in the middle.) Select that noise, then "Noise Removal" from the Effects menu. Click "Get Noise Profile". Now select the entire track (Ctrl+A), and select "Noise Removal" again. Set the slider at 2 or 3, then click Remove Noise. That should get rid of the noise, and the low removal setting should preserve the high end as much as possible.
Pops and clicks need a different approach, since the automatic tool built into Audacity misses quite a few. Thankfully, it's easy. They will appear on the waveform as nearly vertical lines. Select one with the I-beam tool, and zoom in until you can see the individual samples (dots on the line). Now take the pencil tool and draw an even, smooth line over the click ripple. (Make it blend with the surrounding data.) Zoom back out and the click will be gone.
(Yes, I have done this before.
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