So I just got Skyrim today, are there any mods I should get right away or should I just play vanilla?

Any recommendations at all?

Play vanilla. If you wanna get some of the face/body mods to tidy things up a bit then that's fine but I wouldn't recommend changing anything until you've played through vanilla first

In a word: Yes!

Long Answer: The main tool for creating mods (The Creation Kit) has not yet been released. That has not stopped people from making mods already, but in general they are simple or aesthetic changes. Creating gameplay mods without the CK is very tricky, so there are not many of those yet. I would not say that there are any "Must Have" mods yet, but there are some nice tweaks.

Since there are still relatively few mods out there, you can actually glance through all of them on skyrim nexus in a relatively short amount of time.

I wouldn't recommend getting anything before CK is released.

Why? Retextures are mods and don't need the CK at all.

I agree. Some of the retexture mods (armor mainly) look really nice. No reason to not use them on your first playthrough.

Better werewolves and vampires mod. While the transformation duration can't be altered yet, this mod allows health to regenerate, and gives you more health as a werewolf.
Jump higher. Just managed to jump over a Wood Elf. Better than default crap jumping.

Rich merchants (2000 gold instead of 750).
Increased summons (I use summon up to 10 creatures). Still requires using your magicka so not overpowered.
Battle Script. Great mod to populate cities and towns with extra guards.

Play Vanilla. I'm like 78 hours in and I'm still not considering modding at all. Plus, all the mods are mostly minor tweaks and retextures. Though you could use Retextures on your first playthrough, since they don't alter gameplay, they just make the game look nicer. No major mods will be out until the CK is released.

I would say definitely get the interface hard coded key tweaks mod, that makes the menus and keyboard assignments much more agreeable on pc. I consider it more a fix than a mod, and would suggest using it for your first playthrough - http://www.skyrimnexus.com/downloads/file.php?id=88

Check my mod list out if you want to check out some good mods... http://www.gamesas.com/index.php?/topic/1288156-wip-compilation-of-mods/

Im wondering if anyone has figured out if we can change JUST the walking speed in game? I know we can use the player.modav speedmult ## cheat but that changes everything about the PC.

http://www.skyrimnexus.com/downloads/file.php?id=479

The best mod yet: An awesome font mod!

I like this one http://www.skyrimnexus.com/downloads/file.php?id=131

It's really a matter of taste more so than anything else, but I like it.