The software you use to record is the least important part of the equation. No amount of fancy programs can restore information that was not played back or captured digitally.

Get the best stuff you can afford. If you're a smart shopper, you can find good stuff on the cheap.

Playback hardware is SO important. Look on ebay for a nice cassette deck, the Tascam 122 series is a great deck used in a lot of pro applications, and of course Nakamichi is famous for good reason. You need something that gives the best range of frequency and has the least self-noise, etc. Make sure you have the capability to set the output levels of your analog signal, because if the level goes higher than 0dB you will get digital artifacts/noise.

There's a lot of different ways to take the RCA outs from your nice tape deck and make it a digital signal. You can use a DAT deck to convert the signal to digital, and you can use a CD recorder. You can use the soundcard on your computer but keep in mind that the soundcard that came stock is probably not going to get the most out of your precious master tapes. I would give a call to Sweetwater and see what they've got a special on that will fit your box and budget. They are a great place to buy audio stuff from, they totally give a crap if you are happy with what you buy and will walk you through everything.

http://www.sweetwater.com/

So once you've got your hardware set up, the hard part is done. You connect your tape deck to your recording device of choice. Monitor the playback without recording, to set the levels. When you're sure that you won't go over 0dB, leave some safe room for bursts of appluase and volume swells from the music or changing conditions. Pick your sample rate on your recording device (44.1kHz if you want CD audio, 48kHz if you are doing soundtrack for a DVD or something) and hit the red button and then press play on your tape deck. There will be a monitor in your software that gives you the input level - if it goes red (0dB or higher) you need to trash that file and start again.

Some recording applications will automatically correct the DC offset that is induced by your signal chain, and in others you will have to manually do that. Just select the whole wav file and perform the detection/correction using the DC offset correct function. You may want to do some minor editing to eliminate dead space at the beginning and end of a wav file. Once you've done that, open the wav file in CDWave and cut it into tracks. You can compress with FLAC from CDWave or do it later with the FLAC application software. Try to resist the temptation to mess with the recordings - no one can fault you for leaving things the way they were recorded, in the purest form.

Most important, look and listen. Look at your recording - check for pops, clipped waveforms (the tops flatten), or any other strange stuff. Then listen. Burn a copy and play it in your stereo for a while. See how it sounds, if you messed up anything.

Take your time.