Technically you do not need MVC since you have no view to be rendered, but in mvc6 there is just a single controller for both MVC and web api so it may be easier.
as for the routing part you could just make a web api project and use Data Routing Attributes for each method:
[RoutePrefix(“api/Whatever”)]
public class WhateverController : ApiController
{
[HttpGet]
[Route(“GetCandy”)]
[ResponseType(typeof(List<CandyModel>))]
public async Task<IHttpActionResult> GetCandy()
{
return Ok(new List<CandyModel>());
}
}