Good camera for amateur photography?

I would like to take pictures that involve fast action pictures such as capturing a horse running through a field at full speed or what falling and I want the quick action shutter where I can just push the button and it keeps taking pictures. Also I want something with a good zoom I will be taking far away pictures and a nice flash is optional.
Would like to keep the camera under 200 dollars but I have been considering the Nikon J1 so any opinion on that camera would help.

Pentax do some good quality but cheap SLR's.

If you are serious about photography I think your needs require an SLR and a telephoto lens

You are going to need a DSLR to prevent lag time when taking actions shot, but $200 is less than 1/3 of the cost. I would suggest waiting and saving.

Fujifilm FinePix S4000
is the camera I have.
and I love it.
it zooms super far, like crazy far. You can change the lenses or anything and its digital, not film. But i'm assuming you are asking for a digital lol. It has flash, macro(makes things very detailed lol) and mine is a little over 200 but its an amazing camera and worth the 20 extra bucks