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You'll want to maximize shutter speed vs available light, which can be done the following way:
Raise the ISO to max tolerable level (YMMV and so will your camera).
On my D70, it's 400ISO, 800 if I'm really pushing it. Most newer cameras easily do 1600ISO.
Aperture as wide as possible. (Low f-number). With most zoom lenses, you'll get wider aperture at wider angles, so zooming out can help.

You should aim to be able to use 1/60sec and above. Even if it's still a bit underexposed, you can correct a lot of them in the post-process.

In short, buying fast(er) (low f-number) lenses is the easiest way, but also the most expensive.

Some halls offer enough light that you can get away with f4, others I can just about get away with my f1.4 50mm lens, but in most, my f2.8 50-135mm is a perfect match.

If you want to take kendo pictures, then I recommend getting a 50mm. Even if the Cannon f1.8 isn't the greatest 50mm in the world, it will still greatly improve the pictures you take and it will force you to work a lot more on your composition.
Then get a medium f2.8 zoom lens and you can do most stuff.