Hits meaning just requests. In this project I have no public web pages; the requests are coming from an app. The app caches all data when it loads, and then occasionally writes. It only tracks a single record; it's not like a leaderboard, so it's only a single record SELECT (or INSERT if not found), or a simple UPDATE. The initial load of the app is already 10 seconds, and I do the request async, so a 2-second delay is no problem at all. The write is also async, so it's not really a problem (for us) if the response is slow, as long as it's less than the 10-second timeout.
Still, we really don't know what the traffic will be like. We did a similar project last year, which the publisher put on Amazon (they already had leased servers), but I don't have access to the stats.
Unfortunately, I don't know how to compare a shared server with the dedicated ones. The Wiki mentions limits placed on shared servers (http://wiki.dreamhost.com/Shared_server), but not what they are. Complicating matters is that we expect the most traffic to occur upon release. If we go with Dreamhost, I'm sure we'll go for a dedicated server, but I don't know which one.
I suppose no one really knows how much traffic they will get, and always hopes for a lot. I need to ask Dreamhost how fast we could switch to a better server if necessary.