The following are factors which play a part in determining the camera you end up with.
1. Your budget
2. Leisure or Work 3. Experience
We all went the best. Preferable a Leica - a Rolex among cameras. But what we end up with is what is within our budget. This decides whether you would be getting a fixed lens portable or a DSLR. You can get a standard compact one for a few hundred dollars. But the dollars add up pretty quickly for a DSLR because of all the accessories needed.
Work or Leisure If it is for leisure or for tours, those compact ones would be a better choice as it leaves plenty of roof for other stuff in your luggage vs a DSLR with minimum of 2 lenses etc... Of course the end result from a DSLR is way better than a compact in terms of low light performance and resolution. Which is why many are opting for micro thirds which is small as compacts but still packs some of the power of DSLR.
This has got to do with how comfortable you are with handling your camera. If you are just a point and shoot guy, having a DSLR might be overkill as you would not be using 80% of a the features. There are photography courses you could take to for this.
If you are going the way of a DSLR, next question would be the brand to get. Reason is because the lenses and accessories have to be of the same brand. With that said, Canon and Nikon are well established with a wide range of lenses, so either of these would be a good choice.