In case the heading isnt obvious what I am asking is, all else being
considered equal, assume you want to target the first <p> element in a string
of similar <p> elements

You could do it with either:

p:first-child

or

p:nth-child(1)

[remembering that nth-child uses "1" index syntax, not zero index
like an array]

So I am looking for arguments in favor or against one or the other.
Pros or cons.
E.g. which is best for most robust browser compatibility.
Or if you like, efficiency of parsing for the browser.

Which is best practice in your view?

It seems logical to me that the implementation of first-child would just be an alias for nth-child(1). And with that logic, all browsers that supports first-child also supports nth-child. Don't take my word on that though, I'm really only guessing here.

Actually, I just found out that while first-child seems well supported,
nth-child is NOT supported in Internet Explorer (even up to IE8 which is
surprising. No idea about IE9).

Also Firefox below vers 3.5 doesnt support it.

First-child is supported by all browsers except IE6
(but as far as I'm concerned, stick a fork in IE6 cause its done.
I dont support that browser any more).

http://kimblim.dk/css-tests/selectors/

Seems like we have a winner.