Comma after a coordinating conjunction preceding a parenthetical at the start of the sentence

Solution 1:

As Robusto points out in comments beneath the question, there is no universally acknowledged rule governing whether to include or omit a comma after a conjunction at the beginning of a sentence. Robusto reports preferring to include such commas in academic documents, but many other writers and editors would not include them.

In my experience copyediting manuscripts for book publishers (including university presses) and later for magazine publishers, I don't recall ever having encountered a house style that required adding a comma after "And," "But," or the like. To the contrary, most house styles either said nothing at all on the subject or recommended omitting such commas, presumably for the reason that Words Into Type, third edition (1984) gives at the start of its long section on comma usage:

A comma should be used only if it makes the meaning clearer or enables the reader to grasp the relation of parts more quickly. Intruded commas are worse than omitted ones, but keep in mind at all times that the primary purpose of the comma is to prevent misreading.

The argument for including a comma after an opening conjunction is not, I think, grounded in a desire to make the meaning clearer (since the meaning tends to be quite clear without the comma, as Peter Shor indicates in a comment above), but rather in a desire to demarcate with exactitude the boundaries of the parenthetical expression that follows. Why Gregg Reference Manual would insist on such precision at the beginning of a sentence but not in the middle of one is a mystery to me.

There is nothing inherently wrong with using commas to break out parenthetical phrases regardless of where they appear in a sentence: It increases the number of commas in a work while (arguably) not making the sense of the text any clearer; but it's a style decision, and style decisions—if followed consistently—don't need to be justified.

On the other hand, if you don't want to add a comma after a conjunction at the start of a sentence, I don't think that you should consider yourself to be under any obligation to the preferences of Gregg Reference Manual unless your publisher has instructed you to obey it.

Solution 2:

In our English grammar school fifty-odd years ago, the very idea of beginning a sentence with 'and' or 'but' was so strongly deprecated that discussion on how to punctuate a sentence beginning with a conjunction would not have arisen. However, not all authors were of the same opinion on the usage, even in those days, and nowadays one sees it everywhere.

To my mind, it is illogical to place a comma before 'and' or 'but' where the word precedes a parenthetic(al) expression, and I would not do it - nobody would say, "My parents (and in many cases) their friends prefer traditional British food to foreign food" as removal of the parentheses leaves the sentence incapable of standing alone - the acid test, we were taught - so why do differently with parenthetical commas? However, I concede that the practice has been widespread for many years. In Simeon Potter's popular text book "Our Language", written in the 1940s, he does occasionally position the comma before the conjunction - but not invariably. Whatever the style gurus say in the Windy City, I will still need some convincing.