advise on connection please

Ive just purchased a Tacx Vortex smart turbo trainer along with Tacx+ micro dongle for android.

As i would like to join Zwift could someone let me know what i would need to buy in order for me to run Zwift via my pc

All you need to buy is an ant+ dongle for your pc. You can buy them on amazon. I recently bought a vortex smart, and it works great.  

would i also need the antenna

I just use a suunto ant+ dongle and a USB extension cable.