I found an unopened box at my local thrift store with a lightweight LP that has a USB cable intended to send the signal directly to the computer. The box boasts that it will convert LPs to MP3s. It comes with a small CD with audio software and the instructions indicate that this is a version of Audacity. When I send the signal to the computer, I'll use Nero to process it, and there I can save it to something larger and more durable than MP3s.

Once you have the data in the computer then you can massage it, removing hiss or pop, etc. The heavy lifting of this kind of work is in the software. And if you search on "Audacity" in the forum you'll find a lot of chatter.

There's another thread, also old, with a lot more discussion: Help: transferring vinyl to CD or computer.