It would be convenient if there were a cookie-cutter solution that you could apply to any web startup business. Unfortunately, it is not quite so easy. The type of hosting service you need for your startup largely depends on the nature of the business, as well as your short-term and long-term goals.
If you are starting with a very small budget, you can still get quality shared hosting and have no problems hosting your web applications. On the other hand, if your goals are pretty high and you have a good amount of capital to spend on hosting, you may look for a more scalable solution involving a VPS (virtual private server), dedicated server, or cloud hosting solution.
The next issue you should consider is the type of app you want to host. Type in this case could refer to many things: programming language, functionality, design specifications, and even licensing (free, open source, commercial, etc.) For example, if you know from the start that you will be developing with Microsoft Visual Studio and need an ASP.NET platform, it would make no sense to sign up for Linux hosting. On the other hand, if you are used to developing in a LAMP stack (Linux, Apache, MySQL and PHP) environment, you should find a host that can meet your requirements.
If you do not plan to develop your apps at all and need something that is easy to install and manage, you might look for a host that offers easy 1-click script installers or even completely managed hosting. If you already have a proprietary app vendor in mind, you should check with your host to make sure they can support the applications you want to use.
By choosing your hosting provider carefully and considering all of the factors that will form the fabric of your startup, you can get off to a great start and be on your way to success.