This can be a very difficult decision as there are so many types of cameras around.
How much do you want to spend?
The first question I always ask somebody in choosing a camera, is how much can you afford to spend? This is a very important question and you need to be very honest with yourself in answering. The more you spend the better the camera, usually. The minimum spend to get a decent camera and lens is about $800 - $1000. This investment will get you the basic entry level DSLR or Mirrorless camera and at least one lens. If you can afford $1500 - $2000, you will get a whole different level of camera with a much better sensor quality, 2 lenses, or one better lens, and an increased level of functionality and performance. To get into the professional level in terms of camera and lens, you will need to spend between $4000 - $6000. At this level you will get an amazing camera body and one professional quality lens. The increase in image quality at this level is profound, and if you are considering becoming a photographer and competing in the professional market, this is the type of investment you need to make. If you are starting out, my advice is to go for the medium level camera to learn and practice, and then, if you are good at Photography, start to invest in professional equipment.
Which brand to buy?
This is a burning question that many people get wrong. Before you think about the brand or type of camera, you need to work out what you will be using the camera for. If you will be doing a lot of travelling, and don't want ot carry a heavy DSLR and kit around, then you need to go for a Mirrorless camera like the Olympus OMD, or the Sony Alpha series cameras. I have used many of these cameras and if size and budget is a concern I would recommend the OMD. The basic level OMD starts at about $800 with one lens and you can spend up to $2000+ for a better body and more lenses.
If you are into very high image quality in a travel camera, I would recommend the Sony Alpha a7 camera. Incredible detail full frame sensor and beautiful lenses. You will need to spend from $1500 on the body and $400 - $500 on a good lens. The image quality from this camera will compete with a professional image in a camera you can fit into your carry bag. Overall the Sony is more expensive but a better machine in terms of image quality.
If you don't mind a larger camera and acessories in your kit, then go for a DSLR. The 2 brands I recommend is either Nikon or Canon. Which one do you choose? They are basically the same at the various expenditure levels, so I suggest you go to a store and feel them both to see how they feel in your hand. This is important. If you are going to be using the camera and changing settings quickly, on the run, it has to feel right in your hand. I don't have any preference for Nikon or Canon as I have used many models of both brands. Lets look at both brands at the various levels of investment.
Canon entry level. This would be the 750D, 100D with 18 - 55mm lens for about $800. One of Canon's entry cameras, but it has all the functionality to get creative with your image. Just remember with Canon, the smaller the number, the better the camera. Their best camera is the 1D, and their most basic is the 1300D
Canon medium level would be around the 70D with 18 - 135 lens for about $1600. This is a much better camera with a higher image qulaity. The 7D Mkii is an amazing camera with a cost of about $2000 for the body only.
Canon top level cameras are the 1D or the 5D mkiii, or even the 6D. All these cameras are full frame sensors with extremely high image quality, but need to be matched to a professional lens to do them justice. The cost of these bodies only will range from about $8000 for the 1D, down to about about $2000 for the 6D, the 5D Mkiii body is about $3200. Lenses for these bodies will cost from $2200 each to be at the pro level.
Nikon, entry level camera is something like the D3400 with 18 - 55mm lens, costing about $800. Entry level but has all the function you need to learn Photography and get creative.
Nikon medium level is the D7200, which is a great camera and should cost about $1500 with either 2 lenses, or the 18 - 105mm lens, for eg. This camera had amazing functionality and a good great sensor giving very high image quality.
Nikon top level cameras are the D5, or the D810. Both cameras are full frame sensors with extremely high quality images, but need to be matched with a professional lens which will cost from $2200 each. The cost of the bodies are about $9000 for the D5 or about $4300 for the D810.
Get the camera that best suits your budget and need for either travelling or creative shooting.
I hope this has been useful for you. Contact me for more info if you like.