Grats! Modding New Vegas was easily my favorite PC gaming experience to date. I'll be checking this thread to see if you have any troubleshooting problems you need help with. For now, though - Here are the mods I couldn't live without. (Not able to post links, yet. But a quick scan of Nexus will net you these rather easily.)
Nevada Skies. THE weather mod. It's simply amazing. It comes with a toy that lets you control the weather and set it to your liking. It might be out of place, but the Mojave is incredibly atmospheric with a blinding blizzard blowing around you. You can also be boring and just have a region-proper sandstorm. Bah. Also tosses in new textures for sandstorms, rainstorms, adds new radstorms. See it for yourself.
4GB FNV. If you ask me, you NEED this. No question. If you want to pump up your NV with all those fancy texture mods, and extra NPCs - and you will - You'll want this beefing you up. You'll have to launch the game through this exe after you install it, but it is entirely worth it. It fixed all of my memory related crashes.
The New Vegas Bounties series. These mods, (And the rest of Someguy's mods.) Will inject a metric crap-ton of quest content into your NV experience. It's crass, crude, gory, and amazing fun. The story is put together very well, and is inter-connected between every mod. Everything a post-apocalyptic game should be. What more could you want?
Spice of Life. This one adds a lot of flavor into the Mojave via adding hundreds of new combinations of clothes for you and NPCs to wear. Really spruced up my game the first time I installed it, and now I can't go without it.
NCR Rearmament. There's a Legion equivalent of this one that's every bit as good, and by all means you should install both. But since I always play NCR - this one is the one I can't play without. It adds all new textures and models of armor for the NCR to play with. Makes them look like a force to be feared instead of a bunch of GIs ripped out of 'Nam 69.
I have a ton more that have a mandatory spot in my load order whenever I decide another playthrough of NV is in order... but I'm not going to fill half of the page with my post - and I'm sure a lot of them have already been suggested.
Enjoy New Vegas, bud. It's easily in my top 5 favorites. (Unless you plan to play Legion. Then we can't be friends, anymore.)