Luck is definitely the most useful all-round, but it's also the hardest to raise. So most people just ignore it.
In that case, Agility is by far the most beneficial of the other stats, especially if you are good at planning ahead at making the most use of turns. This becomes even more evident once Tidus learns Hastega.
After that, Magic Defense. FFX is the one game in the series were magic tends to do more damage than physical attacks. Later in the game, there will be some monsters who can launch nasty magic chains that can really rip you to shreds.
There's been a lot of debate over the years on which is more beneficial: Defense of Evade. Again, FFX is really the only one of the series were Evade has a significant impact. (This excludes FFVI and its infamous bug.)
Some argue that just jacking up Defense and tanking hits is the way to go. But, with high enough evade, monsters miss enough that it's advantageous to have it higher. The thing with defense over evade is that monsters will still hit. Later in the game, most of them (especially bosses) have nasty side effect attached to their attacks in which case it's better to just avoid them all together.
There's actually an old trick that revolved around abusing Yuna, Tidus, and Lu's grids to jack up Evade really high. The evade slots are set-up such that, with lots and lots of special spheres, you can maximize everyone's evade rather easy. Of course, doing this means you have to play a helluva lot of Blitz to get all those special spheres.
I've never done it myself so I don't know that details. But I have seen videos of people who have. There's videos of a certain late-game boss (considered by most to be the hardest in the game) become laughably easy because it can't hit anyone.
After that you have strength/magic power (depending on who you're talking about obviously).
Then MP and HP. Yuna and Lu are really the only ones who need the HP. Everyone else (Especially Wakka and Auron!) need MP--the one exception is Rikku as she really has no use for MP.
See, the thing about hit points is the effect of raising the defensive stats is, over all, a small increase will go a much longer way. In other words, if you can raise your DEF by 1 or HP by 100, take the DEF.
Also, many of the late game monsters (espeically the secret/bonus ones) use gravity magic or attacks that reduce HP by a percentage, or put you in critical, or even reduce it all the way to 1. In such cases, your total HP is kind of irrelevant. For example, the difference in critical between a Max HP of 5000 and 7000 isn't that much. However, the difference of a defense of 50 and 60 is such that it'll mean whether you survive the next hit once in critical.
To put more of a point on it, at the the time everyone made a big deal because FFX was the first of the series that allowed HP to go beyond the 9999 maximum. However, a lot of us hard-core guys don't even bother with it--for myriad reasons I'll get into if you decide to do the side-quest stuff.