If parts of your solution require custom development, your C#/ASP.Net knowledge will be useful. The preferred goal when developing SharePoint applications though, is to use the tools available to you with SharePoint, and go to custom development as a last resort.

You will have a fairly steep learning curve to develop a proper SharePoint application. If there is no other need for SharePoint other than this application, you're probably best off just making it as a pure MVC app.