The AspDotNetStorefront software requires the following 3rd party components:
.NET framework version 4.0 / 4.5
Microsoft Internet Information Systems (IIS) version 7.0 or higher
Microsoft SQL Server 2008, 2012, 2014 (Express versions are fine, but limit max memory utilized and total database size)
Approximately 120 MB hard drive space for the storefront files (this will increase as product images are added to the store)
Server configuration must allow relative paths
For developers editing source code:
Microsoft Visual Studio 2013 Professional, Premium, or Ultimate (only required if changes are going to be made to the source code)
The memory (RAM) requirements for software of this nature can be a very complex question. AspDotNetStorefront cannot provide a minimum recommendation, as what the software needs will vary hugely based on:
Server type (is this a dedicated server where the majority of the memory can go to your app, or a shared host where you only get a portion)
Number of products and entities on the site
Number of daily visitors
Number of concurrent visitors (1000 visitors per day might be fine if they're spread out over 24 hours, but what if you get 750 at once?)
Much much more...
When evaluating potential hosting environments, it is very important that you have an idea of the answers to the questions above, and work with your host and IT manager to determine what is best for your particular needs.