Chances are (almost certainly, in fact) you'll only need one plan at Dreamhost.
Take the Sweet Dreams plan, for example. That gives you 3 domains, 5 sub domains, 10GB/mo transfer, and 400MB storage space.
Assuming that each of your three sites has its own domain name, that means that you can host all three without adding anything to the Sweet Dreams plan (hence the 3 domains). Each of those domains can be connected to an entirely different directory of files, making it a website completely independant from the other two--unless you tell someone, they can't even tell there's a relationship between the three.
With the available resources, the three sites could average about 100MB of storage each, 3GB/month of data transfer, and even have 5 sub domains each (a sub domain is "something.yourdomain.com"). In fact, each of those subdomains can be an independant site in and of itself--I have several on my plan, for example.
The Sweet Dreams plan resources are more than enough for three average-traffic sites (in the tens of thousands of visitors a month, if you don't have a bunch of pictures or multimedia), and if your sites are small you could even do the Crazy Domain Insane, and just add a 3-domain booster pack, which is a savings of $5 a month. (Personally, I'd buy up rather than down since Dreamhost locks in your pricing, though.)
If you want examples, the following sites, as well as others, are all hosted on a single Code Warrior Plan:
Combined traffic is in the 100,000 visitor per month range and within even the Sweet Dreams resources, for reference.