I have only ever sold my mother's house, so you will probably get much better answers from other people, but here goes.
I frequently look at primelocation and rightmove etc. so I was aware of the estate agents who sell houses in the area/price bracket of the house I wanted to sell. I chose 3 and asked them to come and give a quote. One gave a quote which I thought was at least £75k more than we could hope for, I discounted them. I had a pretty good idea of what houses of that type in that area were going for and I didn't want to put potential buyers off. The other two were similar, but one was a little lower than I thought we would achieve.
I consulted with my siblings, the house was being sold as part of my mother's estate, I was the executor but we discussed things together. One of my siblings had got a Zoopla quote which gave the estimated value as even higher than the highest quote we had been given. It was difficult, but I had to convince them that that was unachievable.
I looked at what each agent would be doing for us, publicity, brochures, viewings, and what fee they were charging. I also asked each one what they thought we could reasonably do to the house to make it more sellable.
I chatted to the agents that came to look at the house. In the end we went with the one that gave the quote in the middle. I thought the quote was reasonable, the publicity etc. was the standard I expected, the agent was respectful and helpful.
It is quite likely that you may not get as much as the asking price when you do sell your house, so just bear that in mind.
So do some homework before you appoint your agent. See what else is on the market in the same area. See what similar houses are going for in the same and other areas, and use that information to give you an idea of what your house could be worth so that you know roughly whether the quotes you get are realistic.