The answer depends on the type of hosting your app might have.
If you’re staying somewhere that gives you accommodation web
shared (Shared web hosting), you are limited to ASP.NET. In this case you would make a web application with a call point (i.e.: a web service), and on the outside you’d need a cron job (a service that accesses a page or web service at specified times).
If you can launch an executable or server service (which can be your personal machine, or a company machine), then those are the pros and cons for each model:
App: you can use the Scheduler, as you said, to call your app. Scheduler plays the role of cron job. The main disadvantage is security... Any person with access and malicious can replace its executable by another Assembly malicious.
Service: you can write the routine of own routine activation, and the service is itself cron job. If the service fails, it can restart automatically. It is much harder to replace your service with something malicious and the authentication/account settings it will use are much easier. The only important disadvantage is that it is a little bit, but just a little, more complex than an executable application. Ah, and you need to be the machine administrator to get it running, but I think in your case this shouldn’t be a problem.
I would personally take the job.