Welcome to the PC! I made the switch from PS3 to PC recently as well, and am loving it.
I'd definitely recommend http://skyrim.nexusmods.com/mods/14950/?, http://skyrim.nexusmods.com/mods/11163/? and http://skyrim.nexusmods.com/mods/26228/? for starters. These mods are the ones I've found have made the biggest impact on my game. I dismissed 'needs' mods like Frostfall and Realistic Needs since I first heard of them, but now love using them. I disable them occassionally - it's just plain annoying to be 'tired' while your character is wandering through ... the location for the final battle of the main quest. And I'd find the game very difficult to play without Convenient Horses!
There are also cosmetic mods like http://skyrim.nexusmods.com/mods/12092/?, http://skyrim.nexusmods.com/mods/13486/?, http://skyrim.nexusmods.com/mods/4929/? and the http://skyrim.nexusmods.com/mods/30450/?. They don't have big impacts on gameplay, but do add quite a lot. The cloaks mods work well with Frostfall - they provide additional protection from rain and snow.
Oh, and: You probably could download it, but why not just wait for the Legendary Edition? It's cheaper, there's no need for slow downloads and gives you plenty of time to plan mods 