Ok sorry- matched grip is where your right and left hand 'match' each other- sort of a fist around the butt end- grab the stick in the natural way and that's pretty much it (with both hands).
The other is 'traditional' where the left hand (if right handed) is flipped over and the stick is cradled between the thumb and hand as well as between the ring finger and middle finger. I guess traditional is somewhat out of favor these days, as most younger drummers learned matched, but neither grip is the 'only' grip. (unless you ask Buddy Rich)
I'm sure you can find good stuff on You Tube on different grips of drum sticks...
Marching I did use much larger sticks (traditional and matched grip) so it is possible, but there you tend to have a higher discipline to the overall playing, and are not as 'free' as you can be with the set. You tend to be 'holding' the sticks more and only bouncing on rolls etc. Drum Corps is the extreme end of the spectrum where stick height off the head is measured for each stroke... Make 10 snares sound like one.
In general (and this is my opinion), you should have a very loose grip- almost dropping the sticks. On the pad, you should hear the wood of the sticks (unless broken) ring after hitting, or your grip is maybe a bit too tight. Try it out (you will drop sticks doing this) and you will find that sweet spot where you are loose, but in control. it does take a while, but worth it. You should not be feeling 'shock' from the sticks, but maybe this is your interpretation of the vibration of the wood...
Then you can relax and play!
But back to the size, if you play traditional, (and you may not) I find that if the stick is the same or larger diameter than my index finger, it feels "big".
Still there is no substitute for trying them yourself! And, to add further confusion, the size and shape of the tip changes the tone on the ride quite a bit as well. While at the store, try different new sticks on different cymbals to hear the difference. (be sure to get permission so the dude in the drum department doesn't have an aneurysm using new sticks for demo purposes)
Finally quality. I pick each pair myself (or check them after I get them in hand). You may see a lot of guys rolling them to see their straight, and that's fine (but has no value in my opinion). What I look at is the grain lines. If you see a lot of run-off of the grain (it does not make it from tip to tail straight down the middle) the area where it is running off is where it is likely to break. I have even had sticks break in my hand at the butt end, due to grain run-off.
This stems from pool cues, which should also have the same straight grain to them, guitar necks, and general wood working over the years. You want very straight grain and if you have it, the sticks will last a very long time for you, making even 'premium' sticks a bargain, because they will out-last cheap sticks that may be of lesser quality stock, and/or have run-off. Then check that each stick sounds about the same played on the counter. be sure one is not 'dead' sounding- they should both be lively have bounce with the same energy return. Play a couple notes with each on a ride cymbal and see (hear) the cymbal sounds the same with both sticks.
A lot of typing over drum sticks, but maybe it will be helpful to you!;)