What is a good photography brand out of Nikon, Canon or Olympus? What are the pros and cons?

If you're speaking of point and shoots, the brands you mention are all good, there is no best. You left out also for good brands Fuji and Sony. What matters on point and shoots are the features each have or have not. What matters to lots of people is how much zoom. There's simple to use fully automatic and also cameras where you set shutter speed. So, read up on this stuff. Read the specs of the ones your interested in, in dpreview.com