Definitely use ASP.NET MVC routing and structure for handling database (sql server) do not combine this with angular or another framework.
stick to Model - view - control, angular only used in views do not override model or control functions and structure leave that to your .net client. So angular is there only in this case for making your UI smoother.
MVC is most based on server side and angular/bootstrap is used client side. Angular and bootstrap are fine in combination to help you creating simple views and customization. for the API I would prefer REST, because of the future functions and implementations. But if you are not planning to use your API in future programma's than I would not recommend. Rest api takes more time than a simple webserver client. For handling rest api client I would suggest
[
RestSharp] quick and simple.
I use Ninject for injections, think this is one of the quickest I have seen so far. I can't see if you really need injections in your project dependence on the complexity of you structure and time you have to make the dependencies. Also autofac or another dependencies framework will work fine ofcourse, think this is user preference and what you already have knowledge of. If you want to use UNI-testing than you will need dependencies injection for sure this will save you allot of time at the end.
Entity Framework wil be the easiest way with a sql server 2014 to implement. If you goal is to not make it complex than I would stick to Entity Framework.