If you're not sure of the type of hosting your business needs, you might want to start small, with shared Web hosting. You can always graduate to a more robust, feature-rich package of, say, VPS hosting or even dedicated hosting in the future. Unfortunately, some hosts don't offer all hosting types. Consider how much you expect to grow your website, and how soon, before you commit to anything longer than a one-year plan. It's worth spending the time up front to make sure that the host you select with is able to provide the growth you envision for your site, as switching web hosting providers midstream is not a trivial undertaking.
A VPS runs its own copy of an operating system (OS), and customers may have superuser-level access to that operating system instance, so they can install almost any software that runs on that OS. For many purposes they are functionally equivalent to a dedicated physical server, and being software-defined, are able to be much more easily created and configured. They are priced much lower than an equivalent physical server. However, as they share the underlying physical hardware with other VPSes, performance may be lower, depending on the workload of any other executing virtual machines.