I think you can start at virtually any series opener and be able to pick things up fairly quickly. It's usually best, though, to start at the beginning of a given actor's "tenure" as the Doctor -- for instance, if you want to jump right into the episodes of Matt Smith, the current Doctor, I'd recommend starting at the beginning of series 5 (2010). Hope that helps!
And... wow, I just realized I'd never posted in this thread. Hi! *waves* I've been a fan of "Doctor Who" since they brought the show back in 2005, and have seen every episode since then. I'm also trying to get into the older episodes, which is a lot easier now that they've mostly been released on DVD. But sadly, my cable plan doesn't give me BBC America, so I have to wait for the DVDs to turn up on Netflix. (It's a pity I can't just choose individual channels for my cable plan -- then I could get rid of ESPN, Fox News, and all those stations I never watch, and just get the good stuff like BBC, NatGeo, and Syfy.)