There is a growing trend over the last few years for developers to use 3rd party libraries to help with web based application design and UI. While these tools can enhance the look, feel and usability of an application, it can quickly become a problem if the library is not a local resource.
Developers are often pressed for time, so instead of importing the required library or scripts, they link to them from the application, and use the providers server to deliver the content. There are benefits for doing this, for example you will always have the most current version etc, the downside is much worse. Your killer application is now dependent on someone else's server up-time, and given the recent experiences dependency's and what can go wrong, I would heavy recommend avoiding this practice.
If you are using 3rd party products or libraries, download them to your server and ensure the source is local, this will ensure that your dependencies are purely local and within your server.
There are literally hundreds of server providers out there, and each one offers something different, but for developers, you need to have control. Shared server hosting can be attractive, particularly when starting out, and the cost is a major advantage, however, developers need control, you need to be able to handle server issues quickly and efficiently or this will damage your business and your client relations.
Get your own server!
The ability to manage and control your own server will be worth the extra cost, if you are not familiar with server management, then get a managed server package. The majority of server packages will come with a web interface for domain and DNS management.
Read up on who you going with, don't believe their hype, and don't believe reviews from a "Web Developer". What you should be looking for is a review of a server provider from an experienced "Application Developer". There is nothing worse than building an app that you spend time on securing and locking down when the server itself has major security exploits. Make sure you server provider will work with you to ensure security.
These providers are out there, and you can get a great package on a managed server for reasonable prices, that will grow with your business.
Finally, if you are an Application Developer, don't get locked into knowing only your discipline, start learning other roles associated to your craft, get into server admin and database management. In the end if you keep learning you will become less dependent on others and be able to identify problems and issues from other areas without the need to call someone.