You don't have to sign anything, when someone whats to buy bitcoin you need to send it first and there's your proof.
BTW, bitcoin sells are not covered by Paypal Seller Protection so you need to trust the buyer to not request a refund.
Yes, the buyer should first send the money to him because when he sends bitcoin to them first the transaction is not reversable but if they send the paypal money to you the transaction is reversable. In fact if he intends to do that kind of business he needs to properly put himself in the right condition, transaction with paypal can be very risky at times.