Are there any authoritative sources regarding which language should be tackled first?
Based on this article on elvish.org, the very simplest answer is that you can't. Neither language is sufficiently complete as to allow someone to actually learn to speak them conversationally, something that Tolkien himself addressed in his letter #380;
"It should be obvious that if it is possible to compose fragments of verse in Quenya and Sindarin, those languages (and their relations one to another) must have reached a fairly high degree of organization — though of course, far from completeness, either in vocabulary, or in idiom... It must be emphasized that this process of invention was/is a private enterprise undertaken to give pleasure to myself by giving expression to my personal linguistic 'aesthetic' or taste and its fluctuations"
That being said, there are various resources that will allow you to become as knowledgeable in the "elvish languages" as anyone else (including dictionaries and lexicons of Quenya and various online courses in Sindarin) but given their dissimilarity with each other and with spoken English, the fact is that there's no major benefit in learning one over the other, nor will learning one first give you a dramatic advantage in learning the other.
I'll post my own opinion on the matter..
I've been learning on my account both Sindarin and Quenya for a couple of years; there is enough material for both of them, so don't worry for it (Use Fauskanger course for Quenya and Pedin Edhellen for Sindarin, both are excellent texts).
Now, about them:
Both languages are gonna be a bit complex because of their grammatical setup; Quenya is based on Finnish (which comes from the uralic-root) and Sindarin is based on Celtic (Celtic-root); mostly of European languages (English, Spanish, French, German, etc.) are based on the indo-european-root, so they are 99.9% gramatically the same. Said that, Quenya is a bit difficult, Sindarin is a hell.
The difficult part in Quenya are the declinations (if you're a spanish/german/french speaker it won't be so difficult, because we have also a lot of declinations in our languages) and in Sindarin are the mutations (there are very very very few in english).
Now, in my opinion.. Quenya is a "Full-Language", meaning, you can express almost anything you want (gramatically speaking), while Sindarin is very weak in that aspect; instead of '100%-specific' phrases, you end up expressing 'ideas' which have to be understood and interpreted by the context (which, again, in my opinion, make it loose a lot of points..).
Making an overall evaluation.. Quenya can fully compare to a nowadays language; you can comunicate everything you could in your own language, while Sindarin is like a 'stone-age' language; it can be used to comunicate basic things easily, but if you try to make more complex sentences, you will see a lot of precission loss and a mess due to the mutations.
I believe the reason why people learns sindarin is mainly because it's the language spoken in LOTR dialogues, because, choosing blindly, i would choose Quenya 100 times.
If you have any other questions, i will be happy to help! :)
It looks like the question is still unanswered.
The question asks for a guide to learn either or both Elvish languages. Now, I don't know of an existing guide, I'll try to offer one here.
The materials on either of them are limited. I think you can't fully learn only one of the two (by fully I mean to learn everything that's available), since the two are related. You'll need a better understanding of the other one to better understand the one you prefer. In fact you will have to dig into sources on Old Sindarin, Primitive Elvish, Telerin, Etymologies ... to learn everything that can be learned, in order to coin new words for example. If you don't already have a preference, I would recommend learning Quenya first, as it's more complete and closer to Primitive Elvish.
The most authoritative sources have to be the original. All Tolkien's published texts that contain Elvish are subject of study. Here's a long list - as you can see, Eldamo, where the list is from, will be a great help for studying the original.
But the original materials are definitely not for beginners. If you want more regular courses, Parma Tyelpelassiva is what you need. It has both a Quenya course and a Sindarin course.
Helge Fauskanger has a wonderful Quenya course on Ardalambion, which discusses every detail of the language academically. Most of Tolkien's other languages including Sindarin are also introduced here at length.
And that's it, when you have finished Helge's course and articles on his site, I think you can continue to study on your own. All the while Eldamo serves as a more updated database (dictionaries and reference grammars) to look up.
Ardalambion doesn't cover the writing system, you can learn how to write the Elven languages with Elven letters instead of Latin here.