To make ASP run under Linux, PHP script files are saved as ASP extensions and are redirected to the PHP interpreter. So it looks like the server serves ASP files, but these are actually PHP scripts.
It seems you are looking to save some money. But I think that you have nothing to worry about. Go for the not expensive windows web hosting and I'm sure that will be great as for your budget and for your project. I recommend have a look at http://neowebspace.com/, which is the cheapest windows web hosting provider I have ever seen.
Neowebspace.com do not offer VPS (that as rule next step). And once you are grow you will need to move on their dedicated server. Anyways they are nice in reviews and you can give them a try.