As a professional photographer, I often get asked about the best lens or camera for taking photos. My usual answer is that it really depends on what kind of photography you're planning on doing. Like the saying goes, "the right tool for the right job". You could probably cut a board in half with a hammer, but it wouldn't come out looking very nice. The same goes for photography gear. So, the first question I would ask is what is the camera for? Is it for travel, family, kids, sports, landscapes, etc...
In this article, I'm not going to make any specific camera recommendations, because that changes daily, and really depends on your needs.
Here are some typical uses for a camera (for a non-photographer), and some tips on what to look for when buying for that use.
For a travel camera, look for something light (like a mirrorless) with a lens that has a good zoom range. You'll most likely want to take some wide angle landscape shots but also have the ability to zoom into something in the distance.
Kids & Family
You'll want something with a wide aperture (the lower the number the better) for two reasons. 1. I find that a lot of personal family photography is done indoors. The wider the aperture, the more light gets into the picture, which is better. 2. Wider apertures are good for portraits because it helps separate the person from the background (those nice blurry backgrounds you see in photos).
For outdoor sports, you'll want something with a long lens so you can capture photos from a long distance. Indoor sports photography is a bit trickier. Without getting too technical, indoor sports photography is hard. You'll need three things in a camera. 1. A camera that performs well in low light since gyms are usually pretty dim. 2. A camera with a long lens to capture activity from a distance. 3. A lens with a wide aperture to let lots of light in.
When buying a camera, there are a few factors you should consider. Those are: weight, size, quality, price, and lens detachability (that's not a real word, but I'm using it anyway).
Weight & Size
To some extent, there is a tradeoff between price & quality, vs weight and size. Typically, the smaller cameras are either lower quality or higher price, or both. If you don't mind a heavier, larger camera, then you might want to look at traditional DSRL cameras. However, if you want something smaller or lighter, a mirrorless camera would be a great option.
Obviously, you want a camera that can take good photos. You'll have to find a balance somewhere (unless you're super rich, then go nuts). You don't need to purchase a $35k camera to get good photos of your family. The $400 model will do just fine.
This one is pretty simple, buy the best camera you can afford within your budget.
No one lens is good at everything. You've probably heard the expression "Jack of all traits, master of none". That applies to lenses too. Some lenses try to do everything and do an average job at it. Some lenses do one specific thing very well, but aren't very versatile. You'll have to decide what's important to you. If you want something that does everything pretty well, and don't want to have to worry about the lens, then you can get something with an integrated lens. If you think you'll want to grow into the camera, and get some purpose made lenses for thing like portraits, landscapes, etc.., then get a camera where you can detach the lens.
Here are some tools you can use to help make a decision.
Snapsort - A tool to help research cameras. They have a good comparison feature to compare the details of two cameras.
Pixel Peeper - This site lets you see real photos from a specific camera or lens.
DxOMark - This site has very detailed (and technical) reviews of cameras and lenses.
DPReview - This site has great reviews, and a nice tool to browse different cameras by feature.
These days, you can't go wrong with a Canon, Nikon, or Sony camera. They all make very good cameras and have lots of options to choose from. There are plenty of other manufacturers out there, and they make some very good cameras. Those three are just the big ones.
Good luck using your camera! Once you get it, if you want some tips on taking photos of your kids, then check out my article on 25 Tips for Taking Amazing Photos of Children.