Well in general, bare metal private servers will be cheapest, followed by VPS (Linode/DO), infrastructure services (AWS EC2, Azure) and platform services (also Azure). It's not an apples-to-apples comparison though.

What I don't understand in Jack's scenario though, is why the application couldn't handle 4,000 pageviews. If its a simple web app, it doesn't sound like anything that wouldn't run on a single EC2 micro instance IF the app is properly designed for high throughput. Caching and static landing pages are your friend.