I was in allan's position a couple of years ago, I already saw this thread and saw the lot of you gushing about the episodes (I think this was in the Tennant time, I remember one of the ep previews about the Satan's Pit). I checked it out by reading some descriptions and episode synopsis, and thought it wasn't for me. Didn't get what was so fun about it.

Then I watched Blink. Got interested in who the doctor was, read some sites about the character, and started downloading episodes from there. After a few episodes from Tennant's run, I saw that the weeping angels are back, but it's with a different doctor. So I downloaded those two eps. and from there, I started looking at Eccleston's season (since I've already seen tennant and smith, I wanted to see another person's take).

I guess it's ideal for people who weren't fans of the classic to start with one of the episodes where the story isn't doctor-centric. I've seen some complaints about Love and Monsters but I think it would be a good jumping off point as well (barring the awkward monster costume). For people who just want something that's uplifting/depressing (depending on how they see the ep, especially the final parts), Vincent and the Doctor would also work.