I know many keen gardeners and some say to use soil-less compost and others say to use soil-based compost.  Their opinions differ greatly but they all seem to use exactly the same compost type for both cuttings and potting.

Personally, I use a mixture of half- and half- between soil-less compost and John Innes No 1 potting compost.  This was as recommended by Alan Titchmarsh years ago and I use it and find it works.  It seems to suit most things.