There's several parts to your question. I will try to address them all in the most thorough manner.
First and foremost, "How many games will I have to purchase to get the whole story ?".
If there is one thing I've learnt about Blizzard in the 12+ years that I've been playing their games, is that there is no such thing as "getting the whole story".
With Blizzard games comes lore. In the shape of game storyline, books, comics, etc, etc. They live off selling their games, and they can only continue to do so by means of expanding the corresponding 'universes'. If what you want is a story with a set beginning, middle and end, you will have to look elsewhere.
Starcraft II is (at least initially) planned as a three part release.
Part 1 is the current storyline, Wings of Liberty. Part 2 will be Heart of the Swarm and will focus on the Zerg. Although the storyline has not been announced, there are expectations that it will revolve around Kerrigan (disclaimer: this is pure speculation, mods please feel free to edit it out). The last part, Legacy of the Void, will center around the Protoss.
HotS and LotV will be release in the form of expansions, which leads to believe that the price tag will be significantly lower than for WoL.
This is not new in the Blizzard way of doing things, if you go back a tad more than a decade, you will remember that the original Starcraft was made up of episodes. They did not use expansions back then (that is until BW), but again, expansions were not common back then and DLCs were hiding far beyond the horizon.
From where I stand, I choose to view Blizzard games as an experience. And indeed, one to be savoured. If you are, however, in desperate need for lore, I would advise you to check out the Starcraft related literature available. Amazon would be a good place to start perhaps.
And if your hunger is still not satisfied, you could also join the forums and ride the creative wave. Many a member discuss potential story lines and plot changes there, and from time to time they get rewarded with some sort of contest (last one had a GTX460 as a prize if I am not mistaken).
Hope I gave you the answer you were looking for. If you need more details, ask, and the community shall see to it that you get them.