So I use a Sony a6000 with a variety of lenses, but my selected camera and equipment has taken a lot of time and money to establish. I really love the camera, and can recommend a few lenses in a variety of price ranges that go well with it. Sony has also released two new models of this camera—the a6300 and a6500—which are the same in terms of size but with slight upgrades in features (though at it’s price, the a6000 is probably still the best investment)
I’m obviously biased toward Sony, having invested a fair bit on lenses, but an entry-level camera in Sony’s mirrorless family is also Wirecutter’s top suggestion: http://thewirecutter.com/reviews/best-mirrorless-camera-for-beginners/
In general, Wirecutter’s recommendations are typically top-notch, so you can explore their full reviews in this category and decide for yourself: http://thewirecutter.com/leaderboard/cameras/
You’ll likely find that the majority of good sources will be recommending ‘mirrorless’ cameras: these sit somewhere between cheap ‘point-and-shoot’ cameras and expensive DSLR types, providing the image quality of a DSLR in the size of a point-and-shoot. It might be tempting to get a point-and-shoot to satisfy budget constraints, but I’d always recommend a mirrorless, interchangeable lens camera for the versatility you get.
As I said to a friend who asked this recently, the best camera is the one you have with you! So much of taking a good photo is down to being familiar with your camera and its strengths.