Hmm. Well, majorly it depends on the kind of website you're launching, what your objectives with the said website are, that sort of thing.
But talking generally, as a layman customer, I would expect my web host to provide three things:
1. Substantial website resources (memory, storage, bandwidth)
2. Competitive price
3. Excellent Customer Support
Like I said, it mostly depends on the kind of website you own. For instance, if you have a website that runs on ASP or .NET, you might want to find out which web host has the best Windows hosting platform. Or, if you're launching a blog or anything running on WordPress, you should keep your eyes open for a web host specializing in WordPress hosting.
Let me know if you have any more queries.