What kind of rice is used in Chinese cooking?
Well in Chinese cooking we use a wide variety actually. Typically speaking...

Medium or Long Grain Rice


White Rice
Fried Rice


Sweet Rice or Glutinous Rice


Sticky Rice (You commonly see this at Dim Sum places in the sticky rice dishes wrapped in lotus leaves, among other places.)


There are others of course, but those are the common ones you'll find since you were asking about Chinese Takeout. The shorter the grain, the more "sticky" it will be. However, that doesn't mean that long grain rice should come out grainy either. I suppose different restaurants will do it differently, around here they generally use long grain rice for "white rice". This is how my mother taught me to make rice:


Wash Rice a few times till there isn't any more murkiness.
Add water till it reaches your first knuckle on your pointer finger when the tip is just barely touching the rice (should generally work for any amount of rice).
Bring to boil, turn to simmer (covered). Check back in 10 to 15 minutes If the water is mostly gone, and it isn't at the texture you like, you can always add a bit more water.
Let it sit for a few minutes after the heat is off.


In China, you'll find all different grains. I've seen both short and long grains, and have seen plain white, long grain rice served as well.