Honestly, the biggest difference is going to be in how clean the records are before she starts the transfer. If she is really concerned about how they sound, she should invest in a good record cleaning machine. That alone will make more of a difference than the difference between most cheap turntables. That said, if her records are scratched and in generally poor condition as most people's are, cleaning them isn't going to do any good. Post processing in software will remove most of the hiss and pops, but it can't do anything about distortion if the record is really bad, or her turntable is not set up properly.
As for the turntable, I would suggest a Technics SL-1200 of most any generation. These are direct drive, extremely easy to set up, incredibly durable, and are able to challenge even the most expensive audiophile turntables at a fraction of the cost. The best thing is that it (like a record cleaning machine, if she chooses that route) will be easily resold for most of its purchase price. The resale on even 10-15 year old 1200's is insane (much like Apple products vs. everything else).
The cartridge is perhaps second only to cleaning the records in importance. Unfortunately good ones are insanely priced, but she should be able to get a good one from Audio Technica, Denon, Shure or Ortofon for a reasonable sum. Purchasing the TT at a local shop will also mean she can have someone set it up for her - which is critically important.
Finally, I don't know what kind of sound card she would use, but she will probably need a pre-amplifier before it goes into the computer - although some software may accept the signal without pre-amplification. These also play a big role in the quality of the sound and choices are many.
Obviously, the easiest thing to do is buy one of those off-the-shelf usb units, because it packages everything - the TT, cartridge, pre-amp, computer connection, and software into one plug and play unit. The results are satisfactory for many people, but if you are serious about the sound quality I think she will be disappointed. The good news is they are probably available from places that accept returns - the worst she could do is give it a go - the alternatives are mighty pricey.
