Is there any specific web hosting provider for AspDotNetStorefront?
No, there is no single specialized web host for AspDotNetStorefront. AspDotNetStorefront is compatible with nearly all windows-based hosting providers. If you see some web hosts claim that they are specialists in hosting AspDotNetStorefront websites, they are only trying to attract new customers. Avoid such web hosts which lie to people from the first moment they talk to you. They lie about who they are and what they can and will do. You should know that most windows-based web hosts can handle AspDotNetStorefront websites. You just need to choose a reliable web hosting service and install AspDotNetStorefront into your account.
What is the most important feature which must be considered when choosing a web host?
Besides providing a full service web hosting package, it is very important that your service have an acceptable uptime (functioning and available for use). It means you can access your account whenever you want to update your web pages, and users can enter your website whenever they refer to your site address. If your hosting service is not uptime it can be catastrophic!

   GoldPuma or Arvixe? Which is more preferred? 

Honestly, our first recommended web host is GoldPuma. Contrary to many web hosts that only accept annual payments, since they are sure about the quality of their services, they let their clients do monthly payments. Over 95% of their customers who start on monthly plans switch to annual after becoming comfortable with their services. Paying monthly allows you to switch web hosts quickly when you find that the current host does not meet your requirements. This way, you are not tied down to a bad web host because you have prepaid for an entire year.