Engine Rebuild

[Elvis]

Well, after several years of babying my very worn 289 in my '67 Mustang I finally bit the bullet and decided to get it rebuilt. To be honest, my wife finally allowed me to get it rebuilt. OK, I'm a wuss - it takes a real man to admit it. Anyway, it turns out that my 289 is really a 302. At least I don't have to worry about the numbers matching anymore. Now, to my question. A friend told me that as long as I am getting it rebuilt, I NEED to put "headers" on it. Excuse my ignorance but what would be the advantage of doing that?
The car is my daily driver. I'm not into drag racing although I do take some delight in showing the high school studs that their low rider Honda Civics are also low performers. Additionally, I like a bit of a throaty rumble - not loud but healthy sounding.
So, my question is, do I go with the "headers" or just stick with the current exhaust system? I need a quick answer so any assistance will be appreciated. E.