You should choose the estate agent to sell your house before the frenzy starts. If you buy and then ask the same estate agent to sell, you wont be able to compare their price or quality of their people you wil be in a hurry. What if you end up buying a house where you think the estate agent is rubbish. (It sometimes happens)
Ask a few estate agents to come to see the house and quote a price. Its not
an exact science, but you can make some sort of assesment of how sleazy/ competent them seem. You can then use the other quotes to ask for a discount from the company you choose.
Also ask for a personal recommendation.
If you can pay off your mortgage, you should strongly consider it, unless you may need the cash to put down a deposit on the new house.