Your choice should be based on:

Your knowledge of their existance in your area.

Their reputation.

Their premises should be clean, well presented and modern looking.

Look for indications of their membership to professional organisations such as the N.A.F.D or S.A.I.F

The charges they will make for their services.
(These vary greatly from place to place ).

People don't usually visit funeral directors premises often and do not know the staff, we do not know how we will be treated.
Everybody has a different picture in their minds of these places but you should expect to find a welcoming homely environment.
You should also expect to find friendly, helpful and seemingly caring sympathectic staff who understand what you are going through, you should expect to be shown to a private room where you would be offered refreshments while funeral arrangements are made.

I would want to be comfortable, relaxed and feel ready to discuss my bereavement with someone who can empathise with my feelings and who can offer sound advice to making the funeral arrangements, not some hardened sales like person trying to take advantage of my grief and make me buy a solid wood coffin.

Ask if you can take a look at the chapels of rest too its not too much to expect considering the circumstances.

Don't feel embarrassed if you want to contact the funeral director for an estimate of costs first. Many people have started to do this, it will generate an image in your mind of who you will be dealing with but at this stage you only need to ask the price of BASIC funeral costs.
You only need to know how much they charge for their services and the additional disbursement costs that are incurred with burial or cremation fees, newspaper notices and floral tributes.

A funeral estimate should outline the cost of providing just a BASIC funeral including:
The removal of the deceased from a hospital to their private chapel of rest, preparation and care prior to the funeral, provision of a basic coffin and fittings, for dressing the deceased as you instruct and for the provison of a motorised hearse and ONE limousine.
They may not include embalming (hygenic treatment), extra limousines or newspaper announcements in this price.

You will also need to know of any surcharges that may be imposed, it has become common for charges to be made if for example the funeral directors invoice is not settled within 28 day's.
You should be informed of cremation or burial fees too, that is:
The total cost of a cremation at a local crematorium including the use of the service chapel and also the cost of medical and clergy/church fees if applicable, (some religions do not make a fee for their services).
Burial fees differ with each cemetery or borough but you will need to know:
The cost of re-opening or purchasing a new grave, service chapel fees and those of the clergy, MEDICAL FEES ARE NOT REQUIRED FOR BURIALS.

Newspaper notices, catering, order of service sheets, monumental work, floral tributes and memorial cards are all extra's, usually provided by third parties at discount to the undertaker and subject to V.A.T @ 17.5%

The funeral director has NO valid reason for not providing an estimate and you have a right as a consumer to ask for one.

If you decide to call at a funeral directors premises it might be worth making a phone call first, this way you can be sure you will be seen promptly and may not cross paths with other people doing the same thing you are.
The funeral staff will appreciate this as their current workload could intrude during your visit. Consider making an appointment with the funeral director to call at your home as you may feel more comfortable in your own environment.
An out of office hours service charge may apply.

Sometimes, people think they are obliged to carry on with the funeral arrangements made with their first choice of funeral director, this is not true, you are not legally bound at any time, however, if a funeral director has provided an aspect of their service to you, they reserve the right to raise an invoice for this and their payment terms will apply.

Funeral directors will make their services available to any area as they are not restricted to the boundaries of their location, some may charge a small fee for travelling out of a forty mile radius for example, but they are flexible and the most professional can almost be seen to bend over backwards to ensure their customers needs are fully satisfied.

Funeral directors build their business upon the relationshps and reputation they have within a community, people use their services because family members or friends have recommended them, but, if you think an undertaker in the next town could provide a more efficient service then by all means contact them. It all depends on who you trust the most to take the highest degree of care with the funeral arrangements you wiil make for your loved one.