"Firstly" or "first"?

Which is more correct?

How do I love thee? Let me count the ways. First, thy eyes gaze deep into my soul. Second,...

or

There are four reasons why all should hail the Hypno-Toad. Firstly, his eyes gaze deep into your soul. Secondly,...

I think either one is OK. Some (American) people object to firstly, secondly etc.

Eric Partridge ("Usage and Abusage") says:

firstly is traditionally said to be inferior to first, even when secondly, thirdly ... follow it.

The New Oxford American Dictionary reports the following note:

First, second, third, etc., are adverbs as well as adjectives: "First, dice three potatoes; second, add the bouillon." Firstly, secondly, etc., are also correct, but make sure not to mix the two groups: first, second, third; not first, secondly, thirdly.

Both are correct, however, there is "overcorrectness" in using firstly because it seems more like an adverb than first.

Go on the length principle: both have the same meaning, but firstly is two characters longer than first. The language will eventually evolve to do without the longer equivalent; I'd use first.

I don't think one is more correct than the other. Though I prefer "First" because "Firstly" sounds a little old English.
The important part is you remain consistent. If you use firstly, you must use secondly, thirdly, etc.

EDIT: I found an exception (with regards to the consistency part)

The older standard is first, secondly, thirdly, etc.The Oxford English Dictionary gives the following quote from Johnson's Dictionary, which didn't include word firstly: ‘Some late authors use Firstly for the sake of its more accordant sound with secondly, thirdly, etc.’

Three answers come to mind

1. Strictly it should be "Firstly", because that is an adverb, and in these quotations it is modifying a clause (i.e. a verb). some English users will feel uncomfortable with this.

2. Practically / pragmatically, it could be "First", because most English users will understand perfectly well what this means, and will not feel uncomfortable with it.

3. Poetically (as in the Shakesperean quotation) it can be anything the author likes, because rules of syntax and grammar are frequently bent or broken for poetic effect.

Personally, I would use "Firstly", for the first reason.

For the record: I'm English, so my English may well differ from American English.