and I will still need the proof of purchase like for all cars?
Yes, you will need proof of the purchase price for sales tax purposes -- have the seller fill out the appropriate NYS vehicle sales tax form, most often the "Affidavit of Sale/Statement of Transaction" . Bring the completed form when you apply for registration and title.
and once the seller signs it over it is mine even if I haven't put in the paperwork?
Once the seller signs on the line for "Seller's Signature," the vehicle will immediately belong to the new owner.