A website development company should be all about YOU - the customer. Not about them, or their aggrandizement - and thus we come to the one thing you can easily check about a website development company to determine if they are the kind of company you want to work with:
Do they insist on, or automatically, put their own link on your website?
You've probably seen it before. Embedded somewhere at the bottom of someone's site in tiny print "Website designed by XXXXXXXXXXXXXXX", with a link back to the website company. I guarantee you that a website development or design company that insists on their own branding on a site that they developed for YOU for YOUR branding does not have your best interests at heart. They are thinking of themselves - not you - when they add that tagline. They should be confident enough in the results of their development effort that they KNOW you will talk about your positive experience with them and tell others. They should be confident enough in their own website, and marketing efforts that they don't have to resort to virally spreading their reputation by embedding it in their customer's sites - frequently without their permission or knowledge.
The only exception I can think of to this rule would be if the website development company is specifically offering a trade, which frequently happens on not-for-profit sites. We will do a development effort for you at a significant discount, if we can advertise our effort on the site. But other than that - there is really no good reason to have someone else's name and branding on your site.
So go look at your own site - does it have your web developer's link on it? Might be time to shop for a new developer. Looking for a developer? Check other sites they've done and/or do a google search for their site name - if other companies have their signature at the bottom, move on. Look more until you find a company confident enough to develop sites without putting their own stamp on them.