At least for iOS and Android, the browsers available are sufficiently robust that a web-based application is probably a reasonable place to start. Blackberry might possibly be an issue, depending on what you want to accomplish, and what features and capabilities you require.
I don't like cross-platform packages, especially not across such diverse platform architectures. What you'll wind up with is a Blackberry app that happens to run on an iPhone, and the odds are that something like that will be close to unusable.
Starting web-based has some definite advantages: it's low-cost, and will allow you to quickly "mock up" and deploy new functionality to all users of the app, and give you an opportunity to collect feedback and do testing that would make implementing the app natively on any given platform a lot simpler.