Cheapest isn't always best.   When you are selling, you want the best price, but more importantly, you want the transaction to go through as quickly as possible!  If they offer a cheap deal, they may not necessarily be able to make sure it all goes through properly.

Don't tell them how much you want for your property.   They are the experts.  Ask them to give you a suggested asking price and a likely selling price, and then why they have arrived at those figures. 

You will need to have an Energy Performance Certificate for the property. Will they charge too much for this? In most cases they should cost no more than about £60

What are they going to be like in checking the buyer's ability to proceed?  Once you have somebody making an offer, the person may not be able to get a mortgage, but this only comes to light several weeks later.  What sort of checks do they make when advising you about the offer?

What do they do to check the chain above and below you?   Do they insist on up to date details from other people, or rely upon third-hand out of date information?

Are there several people in their office who can talk intelligently about your transaction?

Do they pressure you into signing a sole agency agreement for a long period?   There's nothing wrong with a sole agency agreement as such, but one that gives sole-selling rights is to be avoided.  However, if they are confident of selling your house quickly, why should they want to tie you up to an agreement for a long time?   Be suspicious of anything more than 6-8 weeks.

Do they pressure you into having them arrange the mortgage on any related purchase, or to use "their" solicitor for your conveyancing?

If you are thinking of changing estate agents you can fall into a trap where you end up being liable for two sets of commission when you sell, so it is important to take legal advice before instructing a new agent.   If you do not have a solicitor already acting for you, you may wish to Contact Us for advice in this respect.