One Side, Then Cut into Tracks, then Export Selection
With Audicity I do it in the other order: Record entire side, select individual tracks, then export selection as MP3.
I like to record an entire side first, cut off the preliminary blank part created by starting the recording before lowering the needle onto the platter, and then use the little numeric counters at the bottom of the Audacity window with the published song length data on the album cover (or hub label) to select each track, and then use "Export Selection" to create the MP3 of the track.
Then I delete the selection from the original recording and repeat until all the songs are individual MP3 tracks. It goes very quickly.
Word to the wise: Begin the Windows filename of the track with the track number padded to two digits.