Experience and qualifications – just because the word accountant is used doesn’t mean that any qualification is held. Look for a registered firm under a recognised accountancy body such as The Institute of Chartered Accountants in England & Wales [ICAEW], Certified Chartered Accountants etc. If the firm is not registered with a recognised accountancy body, it will not be monitored for professional standards. It may not even have Professional Indemnity Insurance if things go wrong.
Cost – this is a big one, ask the question on how you will be charged. Some firms will give you a set fee, others will charge you on a time basis.
How long has the firm been established? At times there may be long periods between speaking to your accountant; you want to be sure they will still be around when you need them.
Personality – do you feel you can work with the firm or individual, and do you trust the advice that is likely to be given?
Where is the work being carried out? Some firms will outsource the accountancy/tax work to another firm/organisation, often overseas. If this is the case, ensure you are happy with this arrangement.