200 million page views on a page that's almost half a meg in size, connects to fifteen different databases, and the application is written on Rails? Woof.
The first issue you're going to run into is that a 400kb page is obscene. Serverfault's main page, with it set to display 50 questions per page, is 19k. CNN.com runs a whopping 21k, images and all. To even consider running 200 million pageviews a day, you're going to have to get that page under control. 200 million x 400k = 74.5 terabytes. PER DAY. Most places who host, host in terms of terabytes per month, not petabytes per month. You'd be moving into Google territory, only with about 1% of the pageviews.
The second issue you're going to run into is that Rail's isn't easy to program in a way that makes sites scale in a linear manner. I won't go so far as to say that it doesn't scale, but many many people have had trouble with it, and you're going to need to pay extra attention there.
The third issue is going to be your databases. 15? Really? That can't be allowed to stand. You're going to need to look into de-normalization, start working out how to build star tables from the disparate databases, and trim that number down. Databases are the places where Rails has it's problems and you're going to want to minimize the number of connection objects you track at any given time.
Until you've got that stuff in hand, there is no point in looking at hardware or hosting. You can throw as much hardware at it as you like.