I don't know if I should watch Clannad or Death Note first.
It depends on what you watched before and so on. Both shows are very well done and really are completely different. I finally got around to finishing up Nodame Cantabile which is more of a comedy then anything and I'm feeling the need for some action (especially since I was tracking K-On and Haruhi Suzumiya season 2)...
You can't really go wrong with either show.... personally I liked Clannad better, but that's a personal opinion.
Since I'm here.. some more shows to watch Nodame Cantabile (and Paris chapter)
-I'll be the first to admit at first a show about classical music did not appeal to me at all. However, Noda Megumi (one of the principle characters) makes up for everything. The show is funny, and well animated. This show has a simple premise, but excellent character interaction. One Outs
-This show really took me by surprise. Being a guy I like it when I get a little fan service in an anime. However, even though this anime might not have action, or fan service, it has incredible tension in the game of... base ball. This show is really a battle of wits between characters, everyone should give it a shot.
(As much anime as I've seen this is among the only sports titles I've seen as it is possibly my least favorite genre) Black Lagoon
-I'm sure this has been mentioned before but it's worth mentioning again. This show is simply explosive. If you want old style shoot em up action this is your show. It's not going to win any thinking or tension awards but this show is fun from start to finish.