That actor is Christopher Eccleston; he played the ninth Doctor Who, and was the first Doctor of the recent relaunch (I wouldn't call it a reboot, since they are generally continuing where the older series left off, although plenty certainly do) of the series. David Tennant and Matt Smith follow him.
In general terms, there are two Doctor Who series. The "old one" started with William Hartnell in the lead role in 1963, which he held for 3 years before the second Doctor, Patrick Troughton, took over. There's a very important facet of the series you must know: The Doctor is capable of surviving what would certainly kill most other beings, but in doing so his "old" body dies and he regenerates a new one (there's a funny line when David Tennant first appears where he runs his tongue over his teeth and says "New teeth. I'll never get used to that."). So you have, in total, 11 different and distinct Doctors over the years, each played by a different actor.
The "new series" picks up with what you apparently just watched, with Eccleston as the Doctor fighting an army of violent plastic mannequins. As someone new to the show, I do agree strongly with others that you watch this new series first; they take good care to explain everything from the old series you need to know, so while there are a few treats for fans of the old show (e.g. K-9 and Sarah Jane), you're not missing out on anything essential.
As for catching up on the old series, I wouldn't worry too much about it. Aside from the sheer volume of it (33 years!), it's as campy as old sci-fi gets, with the aliens being guys in bubble-wrap sleeping bags leaving cellophane "slime" trails. Of course, if you like campy old sci-fi, the original Doctor Who is the best of the best!