There is absolutely no reason to grab F3 over New Vegas. New Vegas is literally what F3 SHOULD have been. It is a true sequel to Fallout and Fallout 2. The main game is perfectly serviceable without the DLC. If you want a starting point, vanilla New Vegas is the way to go, rather than F3, since there is only ONE thing that F3 does better: Set pieces.
Writing, world building, gameplay, stability, CAMPAIGN are all much, much better in NV. Hell, even the graphical filter is more subtle and less annoying than the one in F3, F3 had a nasty, sickly green look, meanwhile New Vegas has a more bearable "warm" orange filter. Moot point since both can be modded away, but still. Locations and places in F3 were just there because of "wouldn't it be cool?". New Vegas doesn't do that, instead tries to craft a more organic, justifiable world.
As for the DLCs, they are a mixed bag, but all of them considerably better than the F3 DLCs. If anything, the BEST of the F3 DLCs (point Lookout) is comparable to the WEAKEST of the NV DLCs (Honest Hearts). The rest? Blow them out of the water entirely.
Dead Money tries something different, making it survival-horror. It is... flawed, but interesting. It has tense gameplay (particularly in Hardcore mode), and it has the best writing in the entire game, which was already very, very solid. Great characters, great experiments, and definitely worth it.
Honest Hearts is a bit more aimless, since the main plot is very, very short. It rewards exploration, and patience. The main campaign there is underwhelming, but once you manage to find all of the Survivalist's logs, things make more sense, and it becomes a stronger experience. At first it feels like a letdown, since a character that was quite hyped in the base game ends up... well, not as awesome, but it makes sense even thematically, and it is NOT his story, anyways.
Old World Blues is different. The tone is both funnier and considerably more depressing/disturbing than in the other DLCs (except maybe Lonesome Road). Free roam, nonlinear, and its theme is 50's mad science. It ties in with Dead Money, so if you get two DLCs, make it this and Dead Money ( and play Dead Money first. That is important).
Lonesome Road is hard. It is also completely linear. It has great set pieces, hard combat, GREAT NEW GEAR, and an interesting "adversary". It is all about the courier, and it was written as a possible reset button for new entries in the series. It's not the weakest entry in the game, but it definitely felt underwhelming after Old World Blues.
Got OWB and Lonesome Road on release, after getting DM and HH at a discount. That after getting NV for 7.50 bucks. It is EXTREMELY worth it at that price.
Meanwhile, I WOULDN'T get F3 GOTY for more than 7.5 total.