Drifting is nothing like track driving. I'm pretty handy on track, but I cannot drift for toffee! If it's drifting you want to get into, I'd suggest looking at drift-specific days and ignoring track days. If you drift a lot on track, you're likely to get the boot.
I would definitely pay for some tuition as it's a black art that you can't really practise on the open roads for obvious reasons, so well worth going down that route. Personally I'd pay to get trained in the Zed, although you may find something slower (like the MX5s they use at Oulton) much easier to start with.