Why do print prices vary so much? Should I always go with the cheapest?

Printing machines vary considerably in size and the number of colours they can print. Typically presses are 1, 2, 4 and 6 colours. Some are small; printing A4 sheets only, while larger presses can print 16 x A4 sheets at one time.
The variations come into play because a printer with an A4 single colour press can still print a 4 colour sheet by putting the paper through 4 times and changing the ink each time. A printer with a large 6 colour press can print a single colour job as well. Printers prepare their prices using the following costs - film and plates, paper, press time. Film and plate prices are fairly standard within the industry and most printers consider it a chargeable cost only rather than a profit centre. Paper prices vary considerably with quality, also a printer who might have a contract job to print hundreds of thousands of a particular brochure every month will get a very competitive price from the paper mills, he could use the same paper for your job quoting very favourably. It is not always a good idea to specify exact paper specifications to a printer but ask him what he can supply at a competitive price, ask for samples and compare the feel.
Hourly rates of printing presses vary the most, an hour printing for one man working a small single press is going to be inexpensive while an hour printing for three men working a 6 colour press is going to be much more expensive. However, a 4 colour job on a single press may take 4 hours while on a 4 colour press only one hour.
If there are big price differences try to find out more information about size of presses, paper etc to see where the difference lies.
Last of all and the most difficult to detect without trying them out is simply that some printers are better than others. Some machines are maintained better and give a sharper stronger result. Some printers are technically better and can produce a better result. A good printer who employs knowledgeable people and keeps his equipment working well will be more expensive than someone who is trying to do things on the cheap.