For starters, grab the New Vegas Script Extender (NVSE) and New Vegas Stutter Remover (NVSR). The former is the foundation of any complex mod, and the latter will just make the game more enjoyable. For NVSR I'd recommend removing the 30 framerate cap unless your computer is just really awful.
For graphics ''enhancements'' there are a few areas you have options in. A handful of high resolution texture replacement packs; they're RAM intensive and load slower than default textures. Some model replacements for plantlife. Environment normal map replacements that alter the way light affects the ground and rocks. There are also DirectX wrappers (ENBSeries namely) that implement additional effects, but these generally have steep performance costs, and the visual changes made are of dubious benefit; eye of the beholder though.
Weather and lighting mods tend to be fairly benign (gameplay-wise) but can really spice up the appearance of the game.
There are too many bug fixes to name, but I can't think of any that are essential; the game is functional as is, and pretty much anything that causes a crash doesn't have a fix available (in general). If you're getting random crashes near Jean's Skydiving for example, no mod to fix that. =/ You'd be better off simply looking through what bug fixes are available and snagging anything that claims to fix a bug you've noticed before and that annoyed you. Large bug fix collections tend to include garbage changes that you might not want.
Like bug fixes, there are too many gameplay rebalances to name. Plenty of good ones, but I don't know what'd be right for you off the top of my head.
Start off slow; load up one or two mods at a time, make sure they work, then see what else you want to add to the mix. Pretty much the worst thing you could do is download 50, research any compatibility issues between them, think you've got everything set up right, then have an unplayable mess.
Queue