Commas after Conjunctions
I don't know if it is flat out "incorrect", but I do know many style manuals recommend against it.
When I was young, the rule used to be that you are supposed to use a comma between phrases (before the conjunction, not after) if there are more than two things so conjoined. If it is only two, the comma is optional. I'd usually leave it off. You'd only put a comma after the conjunction if there also happens to be a subjunctive clause inserted there.
I had an occasion to look at a more recent style guide, and I believe it said the comma before the conjunction is always optional. I don't have any guide with me right now, sadly.
It is incorrect in most situations, but there are some valid cases when the comma is fine: when it is used to isolate an interleaved sentence, to mark an interposition or to express a rhetorical pause.
Here is a phrase where the comma is not welcome:
So we decided to forgive them.
Our phrase starts with a conjunctive sentence and the so comes naturally first to introduce the conclusion. This is the conclusion of an implied debate that must have taken place some time in the past. The decision to forgive them (the second sentence) is the conclusion of that past debate. No commas here!
But let's introduce another sentence and make the debate explicit rather than implied:
So, after we discussed this at lengths, we decided to forgive them.
The sentence after we discussed this at lengths is interleaved with the sentence So we decided.... We use commas to separate it and, if we want to go even further, we can use paratheses: So (after we discussed this at lengths) we decided to forgive them.
The natural order of sentences would actually be:
So we decided to forgive them after we discussed it at lengths.
The commas can also be used in the same sentence when there's an interposition -- something that brakes the natural flow of speaking to bring some details but still is not a complete sentence:
So, after a long debate, we decided to forgive them.
The after a long debate is not a sentence, but just a detail the speaker is eager to emphasise.
In this case, the commas coincide with actual speech pauses. And again we may use paratheses, but this is a bit extreme and it implies longer speech pauses and a change of tonality as well.
There's another aspect of the "So, ..." -- a rhetorical one. In many cases, the speaker will say "So" and then make a long pause. This is usually used for thinking, introducing a threat etc.
So, you thought you could outsmart us!
Or:
"Where were you at the time of the crime?"
"So, I went to the movies, Jenna and I... and then we went straight home..."
The rhetorical pauses are not necessarily correct from the grammar point of view, but they are useful to let the reader sense the speaker pauses after saying So. A more sophisticated writer would use a pause line — (— in HTML code) instead of the comma.
"So— you thought you could outsmart us!"
There's also the matter of the length of the pause. Comma is more recommended for shorter pauses and the — for longer, theatrical pauses.
When the comma would be utterly against grammar rules and the sentence flow in a phrase, the — must be used. Never write something like:
I wrote the first example, and, then I wrote the second example.
If the pauses have to be passed on to the reader do this:
I wrote the first example— and— then I wrote the second example.