Hi Aphex 12 and welcome
Not sure where you are in the world but I believe a good choice for you would be Cashbook Complete by Acclaim
Cashbook Complete Accounting Software for the Small Business
It is a compact accounting program that handles quotes in an easy way - just as you describe with drop down lists of customers to select from and you can output or edit in Word. You can also keep track of Projects/Jobs.
I have attached a couple of screen shots and there are more on the site.
You can download a full version as a trial copy for free for 90 days and if it suits your needs you can buy it for $US120. It is available in US, UK, NZ and Aust versions.
I think it is simple to use and value for money. You could set up an Access database but costs could be higher if you can't do this yourself and have to contract someone to do it for you. There may be other good softs around too but this is my preference