The best camera for taking selfies and pictures of people

Nikon and Canon and several other brands make good cameras at various price levels. You presumably need one with a "front screen" so that you can line up your selfies well.
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The Canon G7x could be a good choice. Excellent image quality. The LCD flips up for selfies. Tilted up 90 degrees it can be good for photographing others without looking too obvious that you are taking their pictures. Lack of a remote control connection is a shortcoming.

With a 1/1.7" sensor, the Nikon P7800 is better than bridge cameras, not as good as the super-premiums like the G7x. Articulating LCD, 28-200mm zoom range, hotshoe, and compatible with infrared remote.

A DSLR with articulating LCD could be okay. A bit heavy and awkward for selfies. A left-handed hold could work. A wrist strap is recommended. Op/Tech USA makes one suitable for DSLR's.
 The Nikon D5500 is probably the lightest DSLR body that has the articulating LCD. 

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 Remember to use peripheral vision to see the LCD, but look into the lens if you want to look like you are looking at the person looking at the picture.

It's against the law to shoot people with a cannon , except in North Korea...
I think Walmart sells a selfie phone just for that purpose.
If you're not really interested in photography , you won't need anything better...

There's no one best for everyone. I've known people to get rid of their $3,000 DSLR for a cheaper one from another brand because of a feature or two that is critical for their needs. You state that you want to take selfies and pictures of people. Well, that's something that just about any camera will do, and do well.

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 In your case, we can lower the number of options by looking at which are not good for your needs. For example, you really shouldn't even consider a DSLR for taking selfies. It's far too big and bulky. You can also eliminate any camera that doesn't have a fully-articulated LCD screen which is a must-have feature for selfies.
Next, since you want to take pictures of people, what makes one better than another? In short, it's the size of the sensor. As the sensor size increases or decreases, so does the required focal length of the lens for any given angle of view. This change has an affect on image quality in that as you decrease the size of the sensor, your lenses become physically shorter. For example on a camera with a sensor of only 1/2.3" (bridge cameras and smartphones) a 20mm lens has the same angle of view as a 112mm lens on a full-frame 35mm format sensor. So what's the big deal? As the focal length of the lens decreases, the area that you get in focus (Depth of Field) increases. Therefore, someone using a a 1/2.3" format camera will find it impossible to blur out backgrounds which is what you really want to do when taking people pictures.
So this narrows your options to those cameras with a larger sensor (buy the largest one you can afford) and one with a fully-articulated screen. Nikon and Canon do make great stuff, but that's not to say that they make the best of all types and models at all price points. Sony, Pentax, Olympus, and Fuji are also fantastic cameras. All of these 6 brands have cameras that will be the best for certain users. 

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Your criteria of selfies and people is rather narrow. What else do want to do? Do you need exposure control? With cameras that have a 1/1.7" or smaller sensor, you tend to not get exposure control as these are typically simple point and shoot cameras. However, once you're in the Micro 4/3, APS-C formats, then you're getting a much more serious camera with far more control over the image-making process, much better image quality too. I think that the Micro 4/3 format could be the perfect blend of control, image quality, and size too. In M43 cameras, Panasonic and Olympus are your best options.

I'll agree with some of what Frank and Ned say. The DSLR is a good way to go Vs a phone; picture quality is way better. (I guess you could consider a small point a shoot but you would not be able to use the LCD screen as much so less you NEED a very small item, put a pin in that idea)

Large sensor is good but full size is just a LOT to spend; the smaller formats will give you a lot of bang for the buck.

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 I got a DSLR with an articulated LCD screen and it is great for selfies and covert shots. I had used a Hasselblad so I did not have to "look like I was taking a photo" in the direction of someone, but that old thing just made too much noise and what are yea going to do with 120 film today.....so that LCD screen is great to help you now put a camera in a way that it does not make it look like you are taking a photo and/or just get a great angle.

Another item that you may will wish to have is a GOOD zoom lens; I got one that went from 18 to 200mm and it will allow you get that close selfie with the wide angle and has enough flexibility to compose just about any group on the street if that is what you are talking about with pictures of people. Maybe think about a 10 mm fisheye as a next lens; it will be wild and wide for hand held group shots, selfies, and let you get a lot in the field with you in the foreground. Granted you have to see what it looks like as it is not for everyone.

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 One other thing the Nikon has is the ability to pick faces and focus on them in an auto mode. This is good for focus and exposure.

When I've got the Nikon D5300, it is going out of production and the D5500 as Ned noted would be a good pick. However, I've got no clue what you have as personal needs and some time in a store with a good salesman would give you some real world knowledge and the feel in the hand need to make a confident choice. I had been a lifelong Canon guy and only went with Nikon last fall when picking based on some features and what I hoped was an open mind but I still feel a bit of a brand trader.

The best choice is one you make the features I suggest may be found on a number of brands.    
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