Do I send to my Transparent address or Z (Private) address to receive the fork? Or it doesn't matter which address?
You can use a Z address to get BTCP, but AFAIK so far there's no BTCP wallet which supports Z addresses. Maybe it supports them when it's finally released at fork day.
I just chatted directly with btcprivate support; with the latest 1.0.0 GUI Full Node you can send to either t1 (Transparent Address) or to Z (Private) Address as it doesn't matter which as long as you can retrieve your private key for either or.
By default most people are sending to there t1 (Transparent Address) which seems the method considering you can track a transparent address in explorer at time of snapshot.
but again,as long as you can retrieve private key for that address doesn't matter which address you send to.