The most fundamental of requirements is that you find a hosting service provider who can host your site. Hosting primarily means that a HTTP/web server is able to execute in the Windows environment and serve up web pages or data files to the requestor (a visitor). Therefore, you will need to choose a server plan; a dedicated, shared or a virtual private server. Please read my two articles (here and here) on web hosting last month if you need to understand the issues involved.
Storage space made available to you is important as that is the space you can utilize to store all the web pages or the data files corresponding to each page. The trade off is that you need more space if you have large number of pages in the site. Ensure that the provider has adequate backup and disaster recovery plans. Look for uptime guarantees too. It should be better than 99.5%
The next essential item on your list should be the bandwidth made available to you under the service plan. Once the site is set up and hosted, you expect visitors to the site. A service provider provides a connection to the Internet. Each time there's a request for a page the complete data on the page is to be transmitted to the requestor. More visitors would mean more requests for pages. Therefore, over time you would expect that more and more data will have to be supplied to the net at any time. The service provider, typically, will allot a part of his total capacity to you. You must have an estimate of what capacity you are going to need when things stabilize. The bandwidth plan offered should be able to meet this. Alternately, you should be able to upgrade to a higher capacity, when needed. While it does not matter initially, you must be very clear on the bandwidth plan. If you are allocated a limited plan, typically the provider will charge you for additional capacity used. These charges could be significant as your site matures and the number of simultaneous visitors goes up. Many providers will provision unlimited bandwidth these days. Then there are no issues.
Those are the absolutely essential needs for any web site. For e-commerce sites there's an additional need that falls in this absolutely essential category. This is the need for providing your customers with secure payment methods. These need to be certified by trusted organizations for your customers to use their credit cards for purchases. Find out if the service provider will be able to provide you that or if you'll have to organize it yourself. It is your direct responsibility to provide this secure method of payment handling. The service provider may be able to help out and suggest the vendors who could help you. Make sure you are able to meet the PCI standards in securing the payment management.
As one service provider starts looking like any other in terms of what they offer, customer service and technical support could be the most important differentiator. Therefore, you should check around with friends, forums and wherever you can find an opinion on the service provider.