Note that this is mainly for SA2 and SA2:B. It will have SA and SADXDC info though.

Your chao’s grades are very important when it comes to the Chao Stadium You can check your grades at the Doctor’s office (see Kindergarten. Ask for the Medical Chart, and there you go. It should look a little something like this:

Now, the grade will determine how much an animal/chaos drive/fruit (See the Tiny Chao Garden section) will raise the Skill Point total. Some say it doesn’t differ, but it’s been proven, the higher the grade, the more skill points can be gained once your chao increases a level. There are 6 different grades, E, D, C, B, A, and the best, S. The most common and easiest S to get is in stamina. Anyway, moving along.

This is a chart of the number of skill points a chao gets when it's level increases:

Most likely to be:
S | +26, +27, +28, +29, +30
A | +23, +24, +25, +26, +27
B | +20, +21, +22, +23, +24
C | +17, +18, +19, +20, +21
D | +14, +15, +16, +17, +18
E | +11, +12, +13, +14, +15

Deffinatly to be:
+28, +29, +30: This stat is an S-ranked stat
+25 : This stat is an A-ranked stat
+22 : This stat is a B-ranked stat
+19 : This stat is a C-ranked stat
+16 : This stat is a D-ranked stat
+11, +12, +13: This stat is an E-ranked stat
(Thanks to Aster Azul of GameFAQs for this information)

So, as you can see, you don't even need to go to the chao doctor to find out the grades. He's just more precise. Now, to up a chao's actuall letter grade in an area, they have to take that evolutionary path. Say you want to take the B you have in swimming up to an A. You have to evolve that chao into a whatever/swimming chao. This is where reincarnation is key. If you want an All-S Chaos chao, you may have to reincarnate it many times before you make it chaos, just to up those grades.

More to come on getting an All-S chao by breeding!