Recording mini discs is just like the old days of tapes (except rewinding takes MUCH less time!) You still have to record in real time, as you will with any method of copying vinyl, obviously. But the sound quality is very good (for compressed digital sound it's the closest to vinyl I've heard), the disc are small and re-usable and you can record vinyl onto them without a needing a PC.
You can also mess with them, editing out sections, clipping run ins, naming tracks, etc etc.
Best to use a hi-end hi-fi separate, not a portable - convenient they may be but they are too fiddly! Finding one with a keyboard port is essential for easy control of the editing process! They are very cheap to buy on ebay.
I'm giving serious thought to replacing the faulty CD player in my car (the ONLY place I am still playing CDs) with a mini disc rig so I can play my vinyl in the car (sort of) and then I could sell all my CDs and buy more vinyl!