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They have a chart on Serebii under their game mechanics section that shows natures and their effects.

For battling non-competitively, these natures seem quite fine, save for Pidgeot and Charizard.

Calm: Raises special defense, lowers attack

Brave: Raises attack, lowers speed

Modest: Raises special attack, lowers attack

Naive: Raises speed, lowers special defense

Quirky: A neutral nature, does nothing

Quirky natures aren't exactly the best nature for any pokemon.
Even though natures only affect the lowerings and raisings for 10%, you really have to think about the total amount of points a Pokemon could get by the time it reaches 100, or think about what points it could gain in a stat.
10% may not feel like a lot, but think about it. You have to think of IV points, EV training, and that 10% boost/reduction from a nature. All of that accumulates to massive amounts of points....Let's take your Gardevoir for example.

A Gardevoir can reach it's maximum special attack at 383 provided it has 31 IVs in Special attack, has been max. EV trained in special attack, and has a boosted 10% nature for Special attack such as Modest.

Just to make this simple to understand, let's just automatically assume you've gone and trained your Gardevoir already to max EV special attack and it has 31 IVs. Now we can focus on just nature, which is what you're asking about.

The Modest nature reduces Attack by 10% and raises Special attack by 10%. Well, Gardevoir's Attack is s**t anyways; you don't need it. So that 10% Attack reduction does nothing. Win-win situation. That's a brownie point.

Now your Gardevoir has a Quirky nature. It does absolutely nothing! This is actually a win-lose situation. Sure, you get no reduction for any stat. Awesome! Very nice!
But you also get no raise in any stat. Let's use special attack again. For a reminder, let's assume you're all maxed out in IVs and EVs. The max you can get in special attack is 383. That 383 points goes down the drain with a quirky nature because you get no 10% raise. So let's take that 10% raise away.
BAM.
38 points gone from special attack.
The max you can now get is 353. Ouch right?
And that's ONLY Nature. More than likely when people start their games, they just say "I just wanna get through it as best as I can and leave the serious stuff for later." There's nothing wrong with that, but those 38 special attack points can come REALLY handy.

Remember that's just nature, which is all you're asking for, but I'm going to try and help a bit more. This might seem gratuitous.

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Let's assume the worst possible standard now. Special Attack reducing nature, 0 IVs in Special attack, no EV training.
Take this for example:

Gardevoir
Adamant nature ( -10% Special attack, +10% Attack )
0 IVs
0 Special attack EV points.

You get no boost of +10% special attack.
383 - 38 = 353.
Not only that, you have a REDUCTION nature. Another -10%
353 - 35 = 318

Whatever number of IVs you have is what extra bonus gets thrown onto your Pokemon in that certain stat. The max you can get is 31. You have 0. That's 31 points gone.
318 - 31 = 287

For every 4 EV points you get in Special attack, you get 1 point in the final level 100 maximum. The maximum amount of EVs you can get on a stat is 255. (People say 252 because 4 doesn't go into 255)
You have none.
252/4 = 63
287 - 63 = 224

Now I did something wrong in the math there. Gardevoir's actual lowest minimum in Special attack is 229.

But you see what difference between that 383 and 229?
That's 154 points!
One again, that's with ALL real Pokemon factors in play.
Even if you're just going through playing for fun, like we all do, it's still a good idea to get a good nature to help your pokemon out.