Yes you should! Mods are a huge game-changer , especially for BGS games, because there are a lot of quality mods out there.
That said, yeah, for the most part you should give vanilla a go first, and get an idea for a what you like and what you feel the game lacks. (Though if you experiment with mods, you'll find ones that you love that you didn't think you would.)
When you first start modding, you should start slow. You can run a huge mod list without significant CTDs, but only if you're very careful with installation and reading docs. It can get complicated. If you jump into that right away, you'll end up hating Skyrim and modding.
Before you start modding, you should check out gopher's vids. Here's a few that might be helpful:
http://www.youtube.com/watch?v=RxQ1JN_X-_Y (watch all in this series)
http://www.youtube.com/watch?v=xTGnQIiNVqA
http://www.youtube.com/watch?v=t6MxLBcSgkc
In terms of mods you might consider before finishing your first playthrough (though give pure vanilla at least a dozen hours or so):
http://www.nexusmods.com/skyrim/mods/3863/? (I won't play Skyrim without this)
http://skse.silverlock.org/(provides more sophisticated scripting capabilities to other mods)
http://www.nexusmods.com/skyrim/mods/19/? (and search for the unofficial patches for all of your DLC and the hi-res texture pack)
http://www.nexusmods.com/skyrim/mods/3222/? gets the menus out of your way, except when you need them
If you have a powerful GPU with 3GB+ of VRAM, I'd also consider the http://www.nexusmods.com/skyrim/mods/20801/? (or your own selection of HD textures). TPC provides a list and a utility to mix and match around 100 texture replacer mods, which you have to download yourself. But you may want to start simpler, or wait until you've finished a playthrough before doing this (depends on your hardware and general computer experience).
And after you've tried out vanilla, come back and ask for more recommendations.