Seriously. But me being a beginner to Esperanto are all of the six ways acceptable in average chit-chat?

The verb esti accepts predicates rather than direct objects, and it is only phrases of the form "subject verb object" that have six permutations. Predicates in Esperanto restrict the word order, so for "mi estas X", the only two orders that work are that one and "X estas mi", which is arguably misleading. The other four orders (e.g. "mi X estas") don't work because then mi and X would form a single noun phrase.

Regarding the free-word-order issue, which is the underlying issue here I presume, the freedom is there because sometimes it's beneficial (e.g. in relative clauses with an object pronoun like kiun), it lets people use word orders they're used to from their native languages, and it lets people put an emphasis on certain words. The question of whether or not the burden of having to remember to use a compulsory accusative is balanced by the above is an "old chestnut" in the Esperanto community. I personally think it would've been better to have it optional like it is in the otherwise botched Ido, but I'm used to it now, and for me it's not a problem.

Don't forget the two others: "mi Xas" and "Xas mi" (assuming the X in your example is an adjective).

So let me get this. Assuming you are talking about yourself to introduce yourself there are really only two ways to do so such as Mi estas X or X estas Mi? If so then why does Bildoj kaj Demandoj list more than 2 ways?
EDIT: Never mind I got it down.

Ways to say "I am (a/an) X" and "I am [your name here]" are two different situations.

Are we talking about ways to introduce yourself ("I am John") or ways to say what you are ("I am a doctor")?

As far as ways to introduce yourself, yes, there are couple of common ways, but also in English there are at least two common ways to say it.

I am John Smith
My name is John Smith