The first thing you need to decide is are you going to use a freelancer or a business to do your project. Both have pros and cons; the freelancer might be able to give you a more personalized experience and be cheaper than hiring a business, but on the flip side the freelancer may not have all the necessary skills to complete your project and there is less accountability - if they fail to do your project it's easier for them to disappear than it is for a business. A long term relationship would also be easier with a business than with a freelancer.
Location
The location of the freelancer or web development company plays a vital role. You have three options, onshore, which usually means hiring your local web company, offshore, which usually involves a country on the other side of the world and near-shore which is a new term and tries to balance the cost savings with ease of communication. Often the determining price will be the cost. If an offshore company can do your entire project within your budget, but an onshore company can only do a fraction of it then it makes sense to use the offshore company. However, if the onshore company can complete your project within budget then it's usually recommended to go with the local option.
Price
There is some confusion when it comes to price - especially when using an offshore web development company. In short you get what you pay for. If one company is charging a few dollars per hour but most of the other companies are charging more then you should ignore the cheap price - there is probably a reason they are so cheap. Conversely you don't want to pay more than you have to, if a company is quoting very high then you'll likely get the same service as the mid-priced companies so this can be discounted too.
Clients
Before you sign a contract or hand over any money it is essential that you browse through past projects the company claims to have worked on. Even taking a moment to email some of the website owners to ask for an opinion on the company you plan on choosing can save huge amounts of headaches in the long run. A web development company will say anything to win clients (particularly offshore ones!) so you will only get the true story by talking to past clients. If the company doesn't list any client websites then take it as a bad sign and move on!