DreamWeaver Compatiable to DiscountASP.net

Dreamweaver hasn't supported ASP in a dog's age.  Windows hosting caters to ASP.net developers.  So no, that's not an ideal hosting option unless you plan to rebuild the current site from ground up in an ASP environment.

I would go with a traditional Linux hosting plan.  There are plenty of affordable options available.

https://www.pcmag.com/picks/the-best-web-hosting-services

To answer your question simply, any text editor that you can write code in and an FTP solution to transfer the files is going to be compatible with your host. But to the other point already made, DW is not being actively developed and most support on the ASP/.NET side has been minimal for some time and are grossly out of date. You are much better developing in Visual Studio