There is potential evidence for both theories, but it seems more likely that Magical Me is a separate book

There is a passage that can be taken as evidence of either possibility. At the end of one of the Defense Against the Dark Arts classes Lockhart says:

"Homework – compose a poem about my defeat of the Wagga Wagga Werewolf! Signed copies of Magical Me to the author of the best one!"

Now, if Magical Me is just the collection of the other books then all the students already have them. Receiving books they already have would hardly be a good prize. Moreover, Lockhart could have just signed the books they already had rather than giving them new ones that are signed.

On the other hand, if Magical Me is a distinct one-volume book, then he should say that the winner will get "a signed copy" rather than "signed copies".

Of course it is possible that he would give the winner multiple copies of the same book, or that there could be multiple winners. And it's also possible that he would give new signed books rather than signing the books they already have, because a mere signature is not much of a prize – Lockhart had already signed many books for free, and any student could theoretically ask him to sign their books at any time. A prize of actual new books has some physical value, albeit diminished by the fact that it's books they already have.

A passage that supports the theory that Magical Me is one book appears when Mrs. Norris is found petrified. Lockhart there says:

"... I remember something very similar happpening in Ouagadougou," said Lockhart, "a series of attacks, the full story's in my autobiography,

If his autobiography was actually all seven books then he should have said which book it was in (as he does on other occasions).

Additionally when Harry meets Lockhart in Flourish and Blotts we are told:

The crowd cheered and clapped and Harry found himself being presented with the entire works of Gilderoy Lockhart.

Yet a few moments earlier Lockhart had promised him his autobiography for free. As explained in this answer, there is only one other Lockhart book mentioned in the Harry Potter books (Gilderoy Lockhart's Guide to Household Pests). If his autobiography (Magical Me) is the whole set of seven books then it is basically itself the entire works of Gilderoy Lockhart. Thus, there wouldn't be such a reason to say that Harry received the entire works. If, however, Magical Me is a separate one-volume autobiography then there is a very good reason to say that Harry received the entire works, namely that it is telling us a novel point – that Harry did not only receive the one book Lockhart promised him, but he received all of Lockhart's books.

Further potential evidence that Magical Me is a separate book comes from the dueling club. There Lockhart says:

"Now, Professor Dumbledore has granted me permission to start this little dueling club, to train you all in case you ever need to defend yourselves as I myself have done on countless occasions – for full details, see my published works.

If the published works were in fact just the different parts of his autobiography Magical Me, he could have just simply said "see Magical Me" or "see my autobiography", as he had in fact done on other occasions.

On the other hand, there certainly is biographical material in the set of seven books required for Hogwarts, such that it might be redundant to have a separate book as his autobiography. Lockhart says, for instance:

"Tut, tut – hardly any of you remembered that my favorite color is lilac. I say so in Year with the Yeti And a few of you need to read Wanderings with Werewolves more carefully – I clearly state in chapter twelve that my ideal birthday gift would be harmony between all magic and non-magic peoples – though I wouldn't say no to a large bottle of Ogden's Old Firewhiskey!"

There is other evidence that can perhaps support either theory. Lockhart was signing copies of Magical Me in Flourish and Blotts:

GILDEROY LOCKHART will be signing copies of his autobiography Magical Me today 12:30 P.M. to 4:30 P.M.

The Weasleys were waiting on the line to get signed books:

They each grabbed a copy of The Standard Book of Spells, Grade 2 and sneaked up the line to where the rest of the Weasleys were standing with Mr. and Mrs. Granger.

If Magical Me is in fact the set of books that were on the Hogwarts list it is understandable why the Weasleys are on line. They have to buy the books anyway so they may as well get them signed. But if Magical Me is a separate book that is not on the Hogwarts list, it would be strange for the Weasleys to be buying it. After all, they had just complained about not having enough money for Ginny's supplies – why then would they be wasting money on an unnecessary book?

"That lot won't come cheap," said George, with a quick look at his parents. "Lockhart's books are really expensive...." "Well, we'll manage," said Mrs. Weasley, but she looked worried. "I expect we'll be able to pick up a lot of Ginny's things secondhand.

On the other hand, if Magical Me is simply the set of books needed for Hogwarts and that is what Lockhart was signing, then it is hard to make sense of another passage:

"You have these." Harry mumbled to her, tipping the books into the cauldron. "I'll buy my own –"

Here Harry gives the books he just got from Lockhart to Ginny, after waiting on the line. Moments later, Ron and Hermione meet him with their own stacks of Lockhart's books:

Ginny went scarlet as Ron and Hermione fought their way over, both clutching stacks of Lockhart's books.

This implies that they bought the books and got them signed. This would mean that the Weasley's probably already bought books for Ginny, as they were with Harry on line. In that case, Harry's actions are pointless. If, however, Magical Me is a separate book then that is the only one that would have been bought. Ginny would still need her Hogwarts books, and then Harry's actions make sense.1

1. The truth is this might not make sense anyway, because when Mr. Weasley comes over to where Harry and the others are he says:

"What are you doing? It's too crowded in here, let's go outside."

If they hadn't bought all the books yet, why would Mr. Weasley suggest leaving the bookstore?