Hi JF,
I'd recommend developing the application locally as either an IIS or file-system based web-site using VS 2005, and then once you are done copying/deploying it on the remote system. I think you'll find this easier and faster in terms of development.
In terms of the database choice, I'd recommend trying to figure out if you can use SQL for everything. You could then develop using SQL Express locally, and then upload it to SQL Server proper on the shared host server. Most web-hosters are now offering SQL hosting prices in the < $10/month range now -- so it is not as costly anymore to use SQL. SQL provides a lot of feature/stability benefits, so would definitely be worth it if you could.
Hope this helps,
Scott