Actually, now that I think about it, doesn't Left 4 Dead 2 have all of the Left 4 Dead 1 maps now? I think there's no reason to get the first one at all anymore.
Edit: Yeah, just double-checked. L4D2 has all of the maps. The only difference is that Left 4 Dead 1 has fewer Special Infected (which might be a good thing,) but I think that'd be a waste of money. Just get L4D2. More people play it online anyway.
Pretty much this.
It still MIGHT be worth picking up L4D1 if you're interested in the fanmade custom maps for it though.
And yes, both games take place along the same storyline and in the same universe; they just follow different people. However, you do briefly team up with the original survivors in one L4D2 campaign.
EDIT: And yes, there is DLC, but you should receive it automatically. It's free on the PC version.