Welcome to the Elder Scrolls.
As many have stated, it's best to play Morrowind first. I recommend having GOTY version, so you can play through Tribunal and Bloodmoon, both expansions are well worth the price of the original game they are so good. Play that to your hearts content and you probably wont have TIME for Oblivion.
But, after you play Morrowind for a while, I'd definitely check out OB. It's a lot of fun, not as fun as Morrowind, but it's still a great game.
Morrowind has much better storytelling and depth, while Oblivion has beautiful graphics, but it also has a lot of really fun quest. The magic system in Oblivion is also better than Morrowinds, and playing a mage is a lot more fun than it is in Morrowind.
Also, don't play with mods. Just ruins the feel of the game, especially your first time through.
The beauty of TES is that it's great in all it's canon glory, meaning the way it was shipped. The only reason people make mods is because they like to complain and nitpick about certain things and want to change them.
Some mods sure add new content to the game making it more enjoyable for some, but rest assured there is PLENTY to do in Vanilla Morrowind and Vanilla Oblivoin. (Vanilla means original, canon, how it was shipped)