Never say that you will stop your search. If you say that, you will be back here in a couple of weeks wondering why they're so slow to send you the actual written contract. I've seen that kind of scenario play out on here too many times (See this example).
No, instead. Ask that they overnight you a copy of the contract, then you'll make your decision then.
By a copy of the contract, I mean that you need to know the final terms, salary information, starting date, job title, the benefits package, any probationary period, possibly the employee handbook (if the contract refers to it), etc. This way, there are no last-minute surprises. Do not accept anything less than that.
Again, if you're too eager to accept a "verbal" offer, expect to be placed on the backburner and to have some of the terms changed by the time they're written into your contract (just like in this second example).
Let me ask you a question. If you were selling a house, but a nice couple wants you to stop you from showing the place to others to give them enough time to put their paperwork together. Would you? Of course not. At least not without a deposit, a firm price, and a written deadline, this would only incentivize them to delay the paperwork as much as they can, while they continue to look at other houses. It's psychological. Once you remove the possibility of losing you, then you become their backup plan and they can continue searching for a better (or cheaper) option elsewhere with less fear. Do not become anyone's backup plan.