This is all very difficult to estimate, especially when comparing against the intentionally opaque specs provided by shared hosting vendors. That Dreamhost page seems to imply that $15/month is the base price with a very low RAM/CPU allowance. I would not have any confidence in running CBox for a few hundred users on that base plan.
Even though you can’t afford it—but since you asked—I think a better $99/month option would be WPEngine, as noted in this thread:
I’m not sure any hosting plan priced below that is likely to provide enough horsepower for several hundred reasonably active users. As you scale in CBox, the server resource that will quickly become scarce is CPU, as PHP is asked to churn out more and more pages to more and more visitors. That also happens to be the resource that is typically most dear to shared hosts. If you start sopping up all available CPU, your site will hit a wall and your host will insist that you move to a more expensive plan.
It might be possible to do something cheaper if you are able to trade significant time and expertise for it. Something like a 1GB Linode at $40/month could be workable with some aggressive back-end tuning, but there’s no guarantee and, eventually, you’d still outgrow it. Happy to talk further and point you to some resources if you’re determined to go this route.