Japanese comedy can be either downright wacky or very subtle. So I'm not sure which one to recommend you. But first I'd probably recommend you to watch these movies first, see if they are to your liking.
- Koki Mitani's movies like Uchoten Hotel or The Magic Hour are not wacky funny that will make your drink come out of your nose, but it's really funny.
- Kamikaze Girls, a comedy drama.
- Wasabi. Not really a Japanese movie, it's a French movie directed by Luc Besson with Jean Reno as the main actor. But the setting plays out in Japan and it's hilarious with plenty of action in it.
For drama, I'd recommend:
- Mukodono. There are 2, the one that was released in 2001 and in 2003. Both are with Nagase Tomoya. Both are funny.
- Nodame Cantabile is wacky funny.
- My Boss My Hero.
That's all for now, if I can think of more I'll let you know :) Hope they're to your liking.