As said above, Honest Hearts, even moreso than any of the others, stands on its own. It gets some backstory in Lonesome Road, but nothing critical, and there's nothing in any of the others you need to know heading in.
I know you said you're in it for the story, though, so be warned that it's pretty thin on the ground. There are a few interesting characters and the framework of a conflict, but the actual narrative is even thinner than that of, say, The Pitt or Point Lookout from F3. HH's main strengths are as an explore-a-thon that offers some neat (but well-balanced) goodies, as a naturalist/crafter's paradise, and as the most beautiful scenery yet rendered in any Fallout game. It also happens to tie in the most seamlessly with the existing wasteland, though if you're a franchise purist the increasing count of locations unharmed by the great war may grate on your suspension of disbelief.
As a side note, I know tastes run differently for everyone, but I would strongly recommend the other DLC as well. I know you say they didn't sound all that appealing, but the stories they tell, individually but especially as an interconnected whole, are considered by many here to be as good or better than that of the core game itself. At this stage in the pricing cycle, they're well worth the low cost of entry, especially with Steam sales on the way.
