I'm a pretty serious amateur audio engineer. I've done hundreds of conversions of old vinyl records to CD. I don't usually bother with cassettes since their original audio quality is so poor, but sometimes I do if I can't find the music anywhere else.
Anyway, here's my solution. Get yourself a quality turntable with a built-in A/D convertor and a S/PDIF output. This is a semi-pro digital audio format and is less prone to interrupted or "glitchy" data than USB. S/PDIF has its own clock and the streaming is very smooth. USB audio is prone to phase jitter and other ickyness.
My personal choice of turntables is the Stanton ST-100, a heavy duty DJ-quality unit with a good pitch control, 3 speeds, and the all-important S/PDIF output. There are plenty of others out there from Denon, Numark, etc... with similar features. Just make sure you get a turntable with a long (should extend past the spindle) S-shaped tonearm. The models with little straight tonearms (used by scratch DJs) will tear up your records very quickly because the tonearm geometry is all wrong. The turntable should also be fully adjustable, with settings for tracking weight, tonearm height, anti-skate, cantilever, etc...
Most modern turntables have decent built-in preamps and line outputs instead of the old phono-level outputs. Good to know if you're going analog, but again, I highly recommend S/PDIF or optical outputs on the turntable.
Belt drive or direct? The Stanton is direct-drive, and will result in a little more rumble (vibration) in the final recording than a belt-drive unit. If you're a stickler for quiet, find a belt-drive model. I use direct-drive tables because they're practically indestructible and I use mine a LOT. I just slap a high-pass filter with a sharp roll-off around 30Hz, on the tracks to remove the subsonic junk.
Depending on what kind of records you have, get a variety of cartridges and stylii, too. 45s and LPs will sound OK with a general-purpose cartridge, but having a couple different needles on hand (spherical and elliptical) is a good idea. If you're transcribing 78s, you'll need a special stylus with a wide spherical diamond. The grooves are much wider, and an LP needle will rest on the bottom, resulting in ungodly noise.
In addition to the turntable setup, you'll need an audio card which can handle S/PDIF inputs. I have a Creative Extigy. There are literally hundreds of options here, from $120 external USB boxes like mine to sky's-the-limit studio-grade PCI cards and firewire interfaces. Pick up an issue of "Mix" magazine and read the ads. A recent issue of "Mix" also had a fine article on turntable setup for transcription - worth a trip to your local library. Don't just run the analog output through your onboard audio inputs, though. You won't be happy with the results.
You'll also need some kind of audio editing software. My choice is SONAR, but again, dozens of possibilities here. You'll have to edit your tracks since the recording from the record will be one long file, and I assume you'll want to be able to skip through the tracks like a "real" CD. So, you'll have to chop them up into a separated track for each song.
I don't do much fancy processing on my tracks. I cut them up, remove the spaces from the beginning and end of each song, and then add very short, steep fade-ins and fade-outs. That way there is actual silence between songs instead of snap-crackle-pop.
I apply a little EQ, mostly high-pass to remove subsonic garbage and sometimes a notch at 60Hz if there's AC hum in the original recording. If a record sounds bad I'll mess around with the frequency response to taste. I don't usually do any noise removal, but it's always an option if you have the software for it. Again, there are literally thousands of digital audio processing and mastering plug-ins out there. This part is like seasoning stew - to each his own. I also occasionally apply a little gentle compression to make a track warmer and fuller.
Then, all that's left to do is normalize the tracks and export them. Normalization locates the "loudest" sample (highest voltage) in the track and brings it up to 0dB, and brings up all the other samples by the same amount. If you do this to all the tracks, they will be consistently loud and "CD-like". Then export them to a folder and burn them to CD. Stay organized here - export them with file names including track number and song name, and put each album in its own subfolder.
Oh, yes - make sure you clean your records VERY well before recording. The classic Discwasher D-4 system is still the best. And make sure that the recording level NEVER peaks about 0dB during the digitizing process. If it does, do the track over. This is another reason I use S/PDIF outputs - they cannot peak over 0dB since they're already digital. If you're digitizing an analog signal, you have to watch the levels like a hawk and may need to use a limiter if the song has a lot of dynamic (volume) changes.
Happy transcribing!