What's the `Best` Source

[Daniel Jess Gibson]

Which of the three is the best (your definition on a mix of availablity, accuracy and ease of access and canon-ness)
1. The Japanese Subbed/English Dubbed DVDs
2. The English Manga
3. The Japanese manga and the fansubs for it.

[Pale Wolf]

In general?
Japanese source and fansubs/fantranslations. If you can get these before they're licensed, you're golden - a fansub has the advantage of being English enough for understanding, and at the same time you can hear what's originally being said and translate for yourself if the fansub doesn't seem to suit it. That and it's cheap - free downloads are always cheap.
And fansubbers are more likely to stick close to the original material - the Elfen Lied dub did some strange things in one particular speech that I noticed. Culturally they're more in tune with our community - they're targeted towards people who've probably picked up some knowledge of Japanese language and culture (honorifics if nothing else), whereas officially-released sources are generally trimmed down to be understood by the lowest common denominator (ie the person who has no idea what an honorific is).
If you can't get these, then it depends on what canon you're planning to write the story in. Prefer manga? Get manga. Prefer the anime canon? Get that. For 'truth', the ideal is always the original source - whether it started as anime or manga.
Within anime, Japanese subbing is best - it preserves some of the advantages of fansubs. For actual entertainment value, it comes down to the sub/dub debate, but we're talking research right now.

[mondu_the_fat]

For ease of access, anime. English manga is prohibitively expensive (here anyway). Whenever someone asks me how much I've spent for my english Ranma and Love Hina collection some of my friends get a coronary. Japanese manga is loads cheaper, but then it requires being able to read japanese. Chinese-translated manga (which sometimes retains some of the culture better than the english versions do) is even cheaper (mainly because they can be found in 2 1/2-inch formats), but requires being able to read chinese, as well as patience squinting through the damn thing. Anime is much easier to get a hold of, even for those who don't download from the internet, mainly because pirated anime CDs cost around $1 for 4 episodes; cheaper for DVDs (20 episodes for <$2). Yes, this is illegal, but it doesn't take away the fact that it exists as a source.
For canon-ness, depends. Pale Wolf has covered it well.

[lwf58]

There's no quick, absolute answer to the question. Most anime shows are adaptations of manga, but some are not. Some shows have creative control by the mangaka, some do not.
Examples: Ranma 1/2 and Bishoujo Senshi Salior Moon are manga adaptations in which the mangaka did not retain creative control. The anime production teams rewrote characterizations, added new characters, and changed story arcs to suit themselves. If you agree with my definition of "canon" as being "what the series creator intended", then the anime of neither show qualifies.
Tenchi Muyo! Ryo-Ohki is an example of a series that began as video-only, so canon is the anime, not the manga.
Shows like Bincho-tan and Digi-Charat are animated stories that originated from store mascots, so the anime is the canon.
Dirty Pair is an example of material that is more complicated. It began as anime, but the series creator also wrote non-manga novels about the characters that contradict statements from the anime scripts he wrote. An American comic book artist was also given full authorization to write stories about the characters that further muddy the waters.
So you can't just point at a format and say "you only need to look at comics" or "you only need to look at anime". It has to be taken on a case-by-case basis.

[Pale Wolf]

It's actually reasonably simple, as long as you don't insist on 'pure, true canon'.
Just check the canons out. If they have irresolvable differences, pick one and run with it (or merge them together, but that's more making it into something new). If they don't, then it's all viable.

[Alathon]

Which of the three is the best (your definition on a mix of availablity, accuracy and ease of access and canon-ness)
1. The Japanese Subbed/English Dubbed DVDs
2. The English Manga
3. The Japanese manga and the fansubs for it.

Generally, I'd say the original manga, and official english translations of it. With the addendum that in situations that have had disputed translations (such as the scene in which Nabiki extorts Ranma after meeting his mother), I'd look for translations of these specific scenes or lines with context & cultural commentary by fans who live or have lived in Japan.
This being in cases where the manga was the forerunner of the anime; it's gone the other way a few times.