Figure out some of the features you want first. How many mega pixels? Waterproof (almost always means poor low light pictures)? Adjustable f-stop, aperture, ISO etc? Replaceable/aftermarket lenses? Shoot video? Once you kind of know what you're looking for in those more concrete terms, go to a camera shop and play with a few different brands and models that fit the criteria. I've always found Nikon to be the most intuitive for me as far as button location, need to read the owners manual etc. Who knows what brand you'll like.
For reference, I shoot a DSLR and shot about 16gb of photos and went through 3 batteries. Also, Go Pros are great for video, but if you want high quality, printable pictures from the trip get a real camera.