Okay so basically I use Shutter Priority at tISO 3200 and probably underexpose
OR
I use Aperture Priority at ISO 3200 and posibbly get blurry images.
Or you get a better understanding of how they all work together and let their strengths work for you, with out making this too terribly hard.
Sports is my favored form of photography. Indoor shooting, while in some ways more demanding, is pretty consistent when it comes to lighting, once you understand what you have, it is not usually one of the thing that is all that difficult to overcome. At least compared to shooting outdoors in changing light.
First, fast glass is preferred for indoor sports for the obvious reason that it allows more latitude to use shutter speed, aperture and ISO. F 2.8 is really a minimum in most indoor venues to get the settings you want with out pushing you ISO to the limit or not having enough ISO to work. If you have no choice then you push you ISO. Use your fastest glass and crop a bit to get the photo you want. At least it gets you in the ball park.
First thing to do is get to know your venue or venues you are shooting in. Most venues, while having anything from adequate to just above midnight during an eclipse lighting, have pretty even lighting across the court. Unless the custodian is too lazy to get out the big ladder and replace a burnt out light bulb.

This makes it simpler. You should be able to dial in your settings and shoot. I normally shoot manual, and always do indoors. One less thing to worry about.
Get to the venue early and meter the court. It is easier with a hand held meter, but if all you have is the in camera meter use it. Meter the different areas of the court where the action will take place. Find the dark spot, if there is one and set your camera for it. Unless the place is really freaky, you should not have any overexposure issues with other locations on the court.
If you don't trust yourself in manual then shoot AV. In AV you control you shutter speed with your ISO. You want as low of an ISO as you can shoot with, while still maintaining a shutter speed of no less than 1/250th. 1/320th would of course be better.
Set you Aperture as wide as it will go. The difference between a nice sports shot and an outstanding sports shot is capturing the action. That mean just capturing the action. Being able to read Suzie's T-shirt logo when she is in the third row is not what you are looking for. A shallow DOF will make the action pop from the background. In AV a shallow DOF will remain a constant.
Now start moving your ISO up until you have the required shutter speed. 800, Outstanding. 1250, still pretty darn good. 1600 you are good to go. 3200...Still good to go. A properly exposed shot that is in focus with the action frozen with some noise is better than a shot with motion blur or one that is out of focus. Neither of those problems is correctable in post processing, noise can be.
Next thing, practice, practice, practice. The athletes on the court or field do, so should you. Before any season starts, I get with the coachs of the college I shoot for and get a practice schedule. I get out there when they practice and shoot them. Gets me thinking about the sport I am going to shoot, as they all have their own nuances when shooting.
One of those nuances is the players themselves. Get to know them and what the can and can't/don't do on the court or field. Sports photography is about anticipation. If you know who your shooters are concentrate on them when they have the ball. On defense, concentrate on the better defensive players.
Lastly, I tell this to all parents that shoot. If you kid is playing you have only one of two choices. Be a parent and watch the game, or be a photographer and record the action. You can not do both. If you are watching the game you are not anticipating what will occur. By the time you recognize that there was something to shoot, it is too late. That camera should be glued to your face and you should be tracking the action through the viewfinder. You don't care about the score, who wins or looses or anything else except good action. If you do, then you are going to miss great shots. Sports photography is demanding and you have to concentrate on it entirely when you are shooting or you will miss shots. Good luck and have fun.