Do not compromise what had been planned about for the web site just to meet the level of what can just be offered with the cheap web hosting package. Try to search for other cheap web hosting packages that offer the applications needed for the web site.
What good is that account to you when your site is down or the server is overloaded? Research how long the hosting business has been in operation. See if they have recently changed ownership, and if they show positive cash flow.
In general, if you run a business on the web, you will not want to take that kind of risk. Bad support and "down" times have a habit of occurring at the worse possible moments (such as during your peak ordering seasons).