Information is power
In part I have created this list because we don't have slick salesmen to talk our clients into using us. We rely on word of mouth and information comparsion to sell our services. I wish people would ask these questions more often and I'll add a little more detail to help with evaluting the answers.
1) Can I see your portfolio
Do not ever hire a website developer or designer without seeing their portfolio, unless your gambling and know it's they guy/gals first site.
How to police check someones portfolio:
If there all new ask why, If they are only a few for each month ask why, if the newest one is a year old ask why.
2) Who will over see the project and who is accountable
So important, especially if they are outsourcing some of the work. If things go bad or need to be changed you don't want to be the one chasing and playing pass the buck.
The other thing is you want one point of call, that is accessible. Nothing more frustrating that not being able to contact someone for days to get a little thing changed.
3) What is the design process, what happens if I don't like it
Very important. If they say we just make it and then hand it over, beware. There should be a process of interview, collecting info, design concept, artist mockup, draft and re-draft, pre-final check, final check off and revision after completion if needed.
4) Where does the content come from
Who is going to generate the content. If the developer will or can provide the content that can be added value. Beware though no one knows your business better than you a colabrative effort is always better.
5) How will the Billing be handed
I would be concerned with paying someone the whole price up front. 50% Deposit and 50% upon completion is acceptable for smaller builds. However with larger bills and my experience with clients coming to use after a failed project, I would suggest staged payments upon reaching bench marks.
Also find out what happens if they fail to met deadlines and standards. Also understand what your commitment is if you don't or won't pay. Are you liable for all recovery costs, do you retain IP rights or even the domain name.
6) How much will the website cost
Often a developer will only provide the code and no hosting, domain names etc. When you are calculating your costs make sure you add;
7) How will updates be managed in the future
Very important, does the developer have update support. Does s/he have even have enough facilities to handle updates. Experience has shown me one man bands struggle with after sales service. If they are installing a CMS for page management do you have the skills and the time to do the updates. CMS aren't that easy to use so don't just assume you will learn how, ever even.
8) How long will it take to start and how long will it take to finish
Very important to know. Also important to know what happens if the developer goes into over time. What will they do to speed it up if anything. If you have an important deadline not finishing on time could affect you financial and this might need to be written into the contract. I like to see estimated hours work for a project. If your developer is telling you 40hrs work but it will take 6months to complete something doesn't compute there. Like wise if the project will be 50 hrs and they tell you 3 days (we do this some times work 24/7 2 days in a row with 2-3 guys). You need an explaination how/why.
9) What will they do to make the website Search Engine Friendly
Now days without good SEO from scratch created by the developer you might as well not even have the website. If your not seen in search engines you aren't there in users minds.
10) Who owns what.
After the final payment do you own:
My last parting bit of advice is don't get caught up in the moment and jump at the first person who's cheap or friendly. Do some real research. Pick someone who have projects of equal or less complexity in recent times in his/her portfolio. Remember pretty isn't necessarily technical complex. If you want a custom business application and the company only has standard small business Wordpress websites you maybe about to loose some money and time. Like wise if they only have stores with 1-40 products in them, then be hyper cautious about handing over a 200,000 sku store the two are polar opposite in skill set required.
There is no regulating body for website developers, so portfolio, professionalism, infastructure are the only measures. If your developer lives with his Mum and drives an old beat up Hyundai, but tells you hes the new Web Jesus with lots of experience. The two don't compute!