There are a number of factors that should determine what kind of hosting you should procure when developing your website. The fact that you could get hosting for as low as US$3.99 a month should not be your main reason. I have had clients come to me saying that they already have the hosting aspect sorted. However, their site requirements exceeded what their hosting package offered. I always recommend, therefore, that you consult with your web developer first before rushing out to get the best bargain.
Factors such as number of email accounts required, programming language, number of expected concurrent visits are critical in determining the type of hosting you should go for. How easy would it be to transfer your site, has the hosting company been hacked previously and how accessible is site support are some questions that should be answered during your decision making process.
My recommendation is to allow your web developer to handle this aspect for you as part of your web development support package. It would be a major headache, for example, if you have to run your business and at the same time worry about why your website is no longer working because the cheapo webhosting package you arranged all on your own. If this is not already included in your support arrangement with your developer then, trust me, it will cost you much more in the long run.