I'm planning on hosting 3 or 4 WCF/.NET 3.5 REST webservices to be used by a new iPhone application.
I've heard good reviews about DiscountASP.NET (http://www.discountasp.net/index.aspx), but I'm pretty ignorant about shared hosting performance. At the same time, I think it's still early to pay $90 a month for a scalable Amazon EC2 server instance.
So, any idea how many hits/month would a shared hosting website handle?
They are all different. It depends on how much bandwidth they are giving you. (GB/Month is a typical metric).
I would say that hits per month could range in the low hundred thousands without causing major issues on many managed hosting. It all depends how intenst your WCF services are. The advantage is that many managed hosting facilities will allow you to dynamically add more hosting power to your site. (For more $ obviously).
It depends on how good your shared hosting is. To determine simultaneous users, you can try to benchmark the performance of your server by hitting with many requests.
Your host will likely yell at you if they see you using a lot of your cpu. For web services, bandwidth isn't so much an issue as is your cpu/memory availability.
You should be more concerned about simultaneous users instead of hits per month. You want to be able to handle any spikes in traffic. Shared hosting is less predictable because you don't control the usage of the other users on the machine.
I would say if you're starting out, shared hosting would probably be fine, just monitor it and upgrade when you see decreasing response times. Your host will probably let you know when you are affecting the performance of everyone else on the server.