Any of the entry level DSLR cameras will provide you with all of the features you need.
Canon and Nikon are the most popular and have a larger selection of lenses.
I suggest you start with one of the kit lenses.
After you have used the camera for 6 months you will know if you need or want more lenses.

You can use the camera in Auto mode until you have learned how to use the manual features.
Those features will let you get excellent results on those difficult shots.
The more you know about photography, the better your results.
Attending a class in photography will be worth the time and money.

To pick a camera, go to a store where you can get your hands on the camera.
See how it feels in your hands.

For ballroom dancing photography, first try some shots with the kit lens.
If you need a brighter lens, look at the non-zoom 50mm lenses.
Some are as low as $85.

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