Okay, I'm going to give a slightly less technical answer here... and a bit provocative.
The real camera resides inbetween your ears, meaning that if what you see with your eyes cannot produce a good photo with just about any equipment, you may have in your hands, you're lost.
I remember I once saw a documentary about a fashion photographer, and when the model saw that he was using a small compact camera, she thought he was teasing her, but THAT was his work camera. And he did make some good shots of her.
So the most expensive camera is not necessarily what will make you happy. Decide how much money you're willing or capable to pay, and then research which options you have.
I'm happy with my Sony DSLR camera, but sometimes it's too big to bring for example going to a party, so I just use my phone camera, which is good enough for that purpose.
Now you said fast moving objects, and like others allready pointed out: a digital SLR where you have the option of exchanging the lenses.
IMHO the manufacturer name ain't the most important. If you have the option then try a photo store and ask for permission to try out some different cameras with different lenses. Ultimately, you will have to make the decision, which camera it's going to be anyhow...
Most great manufacturs have a variety of extra lenses to purchase afterwards. Check those options first. The kit lenses which you can buy together with the camera house may not be the prime lenses, but they do work as a start, and you can then slowly expand the equipment with extra lenses over time. A good lens provides a big aperture (low number like 1.8), kit lenses are often at 3.5 to 5.6 for a 24-70mm zoom. If the focal length is fixed to something like 100mm, it works better with the light available, and the lens is as such then faster working.