A few thoughts and queries on the punctuation of "not" phrases.

I believe it's a rule to have "not" phrases set off by commas in writing, such as in "I decided to buy the blue shirt, not the red one."

I have a few questions in regards to what happens when a conjunction is added before the "not."

First of all, taking the above example, if an "and" were to be added, would there still be any need for a comma? I don't think there is, but I'd better check.

"I decided to buy the blue shirt and not the red one." — Is this correct?

Secondly, there seem to be times when the comma should be omitted and other times when it shouldn't.

"He was happy but not content." — I don't think this should have a comma.

"He smiled over at me, but not in a polite, friendly way." — It seems to me as though it should.

I may be wrong, and please correct me if I am, but I think it has something to do with the phrase in the second example being purely descriptive of the thing mentioned before; it's saying what kind of smile it was. Here is another example along similar lines.

"He was good-looking, but not in the traditional stylish way, more in the rugged sort of way."

Again, I think a comma should be applied here, but I'm not sure if it's considered correct.

Am I right in any of this, or should I omit commas like the ones in my last two examples in the future?