An 'on-going' application implies that it already exists as a standard Windows Server/IIS/ASP.NET/SQL stack (however standard that may be). Moving it to Windows Azure has distinct and valuable advantages, but these need to be weighed up against the cost to migrate the application to Windows Azure. While you may find that there it is reasonably easy to get up and running in demo mode, the application would not have been architected with Azure (or any other public cloud platform such as AWS) in mind. Don't take too much heed of the 'easy migration' markitecture, make your own informed assessments.
As far as other platforms go, Google AppEngine doesn't play with .NET and AWS, while an awesome platform, doesn't have a good story for SQL Server (where you have to roll your own). <1000 daily visitors is not many, and doesn't need all the scalability offered by public cloud platforms (where 1000s per second is the problem domain), and may not justify the costs. Without knowing much more than your brief description, I would recommend that you go with traditional hosting and co-location. Perhaps use the cloud for add-ons, such as microsites, and find out what needs to be learned before your throw you lot in with a PaaS paltform.
Note: I am passionately pro public cloud and have been recommending and working with it for years. I just think that there are many cases where the public cloud is not the best option due to the costs and risks measured against business value