Commas after coordinating conjunctions at the beginning of a sentence?

Question

I asked a question like this before, but I didn't give my reasoning. I'm asking about the comma after "and," "but," "or," "then." I have the idea that if you begin a sentence with either one of those words, and if it's related to the sentence before it, you should place a comma after it. Here's what I mean:

Instead of writing this:

"I went to school, and I talked to my friend Daniel."

You could write it as this:

"I went to school. And, I talked to my friend Daniel."

In that sentence, I feel like by adding a comma after "and" would make the sentence seem related to the one previous said. Here's another example:

Instead of writing this:

"She's going to the store first, and then she'll pick up the kids from school."

You could write it as this:

"She's going to the store first. Then, she'll pick up the kids from school."

My question is asking if this would be a good a good thing to do, add a comma after a coordinating conjunction when it begins at the beginning of a sentence and if it's related to what was said before. Two more example:

Instead of writing this:

"She used to work at a restaurant, but now she works as a teacher."

You could write it as this:

"She used to work at a restaurant. Now, she works as a teacher."

Instead of writing this:

"You can choose to go to the park, or you could choose to go to the beach.*"

You could write it as:

"You can choose to go to the park. Or, you could choose to go to the beach."

Answer 1

When a comma is placed after what would otherwise be a coordinating conjunction at the beginning of a sentence, it indicates that the word in question isn't being used as a coordinating conjunction but rather as an introductory modifier, specifically, a conjunctive adverb. When you put a comma after an introductory "but," it takes on the adverbial meaning of "however"; after "so," it takes on the adverbial meaning of "therefore"; after "and," it takes on the adverbial meaning of "also"; etc. This usage is somewhat controversial grammatically, but it happens with such commonality that it can't go unacknowledged.

When the comma is left out, of course, then it's clear you're using the word as a coordinating conjunction to introduce a coordinate clause, which is a type of main clause and so can stand on its own as a sentence. Since the rules of grammar require that you never use a comma after a coordinating conjunction, it's irrefutable that that is the manner in which you are using the word, not as a conjunctive adverb.

By the way, "then" isn't a coordinating conjunction. There are only seven coordinating conjunctions. They are: "and," "but," "for," "or," "nor," "so," and "yet." "Then" is a subordinating conjunction. When it appears at the beginning of a sentence with a comma after it, it is an adverb.

Answer 2

I think this is a question of style. Try saying it out loud, and if you kind of sing your conjunction and there is an audible comma-type sing-song inflection, then write it with a comma. If you find yourself pronouncing the sentence with a pretty flat voice and no big pause, write it without a comma.