Okay, I haven't played in a while nor finished off Skyrim yet. I've been distracted with some other things. I didn't realize that there are a number of mods for the game out there. I'm basically playing an archer/mage type character.

What would be some of the no-brainer mods to get? If I only got 1 or 2, which ones would those be?

http://skyrim.nexusmods.com/mods/9286 is my personal favorite, it changes Skyrim into the game I would have preferred it being.

This is all very highly subjective. And it will depend on how you feel about script extenders as well as what you want out of the game.

If you're going to get ONE mod, get Sounds of Skyrim, the dungeon version. If you're okay with a script extender, get the popular UI replacement.

I prefer mods that add non-ridiculous weapons (like Weapons of the Fourth Era, I think is the name) and I don't go anywhere without a body replacement mod (there are two very popular ones, but you'll have to search that yourself on the nexus).

SkyUI (http://skyrim.nexusmods.com/mods/3863) is a usually go to interface replacement. It's not entirely done, but in general it's a huge improvement over the default interface.

Unofficial Skyrim Patch (http://www.darkcreations.org/forums/files/file/205-unofficial-skyrim-patch/) fixes a bunch of stuff the official patches don't. No real reason not to have it I suppose.

A Quality World Map (http://skyrim.nexusmods.com/mods/4929) does what it says, replaces the world map. Not a huge deal, but I honestly can't remember what it looked like beforehand, and see no reason to go back to it.

Cloaks of Skyrim (http://skyrim.nexusmods.com/mods/12092) also does what it says. It seems like a minor deal, but even if you don't wear the cloaks yourself it's a neat touch to see randomly distributed to other characters.

I'm using a ton of mods in my current game, but these four have pretty much been in all of mine.

There was just a thread about mods for mages. You can find it http://www.gamesas.com/topic/1401294-playing-a-pure-mage-mod-necessities/

I'd second the mods zherok named. They're all extremely non-intrusive; they improve the game experience without calling attention to themselves. If you only want a handful of mods for a start, pick these four.