My reason for not going with a PC is the amount of time it takes to edit each record. I tried that route with some cassettes and for me the benefit from the editing (removing noise, getting rid of bad sections) was just not worth the time. I've recorded a few cassettes directly to a new DVD/CD recorder and have been very satisfied with the ease and quality of the process. If recording my vinyl works as well as recording my cassette tapes, I'll be perfectly happy.

Having a real DVD/CD recorder in the system makes the process work a lot more easily. The CDs it produces play just fine on my separate, higher quality DVD/CD player. (If I had golden ears I might do it differently but these 60-year-old ears were never golden at their best!) My recorder is about a month old and I will begin recording my vinyl when I finally get around to getting a supply of record cleaning fluid so I can get the best out of them. If anyone is curious, I'll be happy to describe my results.
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Onkyo 886, Outlaw 7100, LFM-1
Allison Ones F/R
Gallo Nucleus Micros surrounds
Outlaw LCR center
Oppo OPDV971H DVD
LiteOn 5005 DVD recorder
SA 8300HD/DVR STB
Dual 1219 phono
Ion Tape2PC USB
Harmony 620
Samsung HLR5078W