Can it handle 1000 visitors per hour?
Totaly depends on service provider, they will clearly tell you what is the bandwidth for certain hosting package.
Most sites don't have this much traffic and yours may not either, especially at the start. You need a profile of how much activity would be associated with each user. 1000 users doing a single short query in an hour probably isn't a problem. If it is 1000 users who will all be active for an hour with a lot of bandwidth, cpu and database activity for each one, then it might be a problem. You might want to share the profile with some web hosting companies and see what they think.
If you realistically expect a lot of users and activity (but not immediately) then you may want to start with a shared hosting package with a web host who can move you to a dedicated server if you reach the point that you need it.
You might find this blog item helpful"
It depends on the hsot but more it depends on the site, if the site is made right then you can over 100k a month, about 3000 unigues a day. This is a massive site that is ran at SNIP the same host I use. Most high ends hosts can handle it but hosts like godaddy or hostgator will boot you off for overloads.