The good news is that, now, all of the surviving complete stories are currently available on DVD (except for "Terror of the Zygons"). So it is possible to absorb pretty much the entire series in order, story-by-story if that's what you want. It's just going to be expensive since you'll actually have to buy the DVDs. (List price, that's anywhere between $10 & $40 per story, depending on the story.)
Checking right now, only 22 stories are available via Amazon Instant Video (at least on the American version): "The Aztecs," "The Tomb of the Cybermen," "The Mind Robber," "Spearhead from Space," "The Three Doctors," "Carnival of Monsters," "The Ark in Space," "Pyramids of Mars," "The Robots of Death," "The Talons of Weng-Chiang," "The Ribos Operation," "The Pirate Planet," "The Power of Kroll," "The Armageddon Factor," "City of Death," "The Leisure Hive," "The Visitation," "Earthshock," "The Caves of Androzani," "Vengeance on Varos," "Ghost Light," & "The Curse of Fenric."
Now, if you have Amazon Instant Video, that might be a slightly cheaper option. It's only a limited sampling of stories but most of the ones listed there are considered to be among the best. You might want to try them and decide whether or not you want to invest further by buying the DVDs for some of the more obscure stories. Or whether or not you're still interested in all of the Doctors or if some of them hold more interest for you than others.
What can I say? It's 26 seasons of very expensive television. But I've been collecting the DVDs for the last 9 years now, and I've enjoyed it a lot. But damn is it expensive!