Hey the answer is all dependant on what you use it for, Anything that is moving quite fast (such as a horse) you may want to use a DSLR because it has manual modes that give you the liberty of slowing the shot down. The cons for DSLR's are that they can be rather large and they are expensive, the cheapest Canon is the T3 for about 399$CDN and it comes with a standard lens. Canon Rebel T3 / 18-55mm Kit - Price Comparison - Canada - Digital Cameras
If you were to go through the DSLR route I would recommend either Canon (my favourite) or Nikon because if you decide to upgrade or buy new lenses or really anything further, they have a much larger selection of higher quality products. Some of the cheaper companies (although I would not highly recommend) are Olympus, Pentax and even Sony.
If none of this is what you are looking for you can buy a point and shoot camera but make sure it has manual options otherwise you may always get blurry pictures if you don't have enough light or the sensor doesn't accommodate high ISO's or you might get a cheaper processor so they will be grainy.
Take it from me, I shoot a lot of fast moving photos (mostly sports) that having a DSLR is worth the extra money. My kit has costed me thousands of dollars and I don't regret buying any of it!
Hope this helps!