I have a Sharp dual cassette deck similar to yours. I take the line out from the deck and send it to the stereo input jack on the Tascam DR-07 mkii and record directly to MP3. I use Reaper if I want to split the MP3 into individual songs or make adjustments, but it does take some time.
Assuming you have one or have access to one, a standalone CD burner will work as well (this is what I would do - but because I have one). I would also record them as WAVs first and then make mp3 versions so you still have a lossless copy of the files.