It's difficult to provide a fair assessment on a vehicle without seeing it in person. You should check out these sites to get an idea how much that Z is really worth:
Official Kelley Blue Book New Car and Used Car Prices and Values
NADA Home Page
Assuming the car really is in great shape, fairly priced, and you're set on purchasing it, you need to:
1. Decide how you will pay for it (with or without financial assistance)
2. Get the bank check, personal check, or money order ready for the payment
3. Get insurance on the vehicle starting the day you take delivery
4. Go to your local DMV to get a temporary plate prior to taking delivery (so you can drive it back)
Just ask the DMV folks what you need to get the vehicle registered. It's usually just the Bill of Sale for tax purposes, proof of insurance, proof of title (if applicable), proof of lien paperwork (if applicable), and some sort of vehicle registration transfer form.
It seems confusing, but it's really simple. I would start by giving the DMV a call for all your questions. Of course, make sure that Z is the right one for you. Maybe I'm forgetting something, but I'm pretty sure that's the gist of it.