I have been a pretty serious amature photographer since the late 1970's, so I'll throw a few tips out there.
$$ - How much are you willing to spend? Todays mega zoom, image stabilized point & shoot cameras can take very nice pictures, in most conditions. If your demands are not high, and you are more interested in "snap shot" quality photographs, they might work for you, especially if you are new to the game. As your experience grows, you will learn the fundamentals, and learn what features are important to you, and what you find to be lacking, because....
No point and shoot will ever equal the flexibility and picture quality of a good DSLR system. Features like sensor size, low light ability, shutter lag, FPS (frames per second), ability to auto focus quickly and accurately, track a moving subject, and much more, all favor the DSLR.
Many folks are attracted to the mega-zoom built in lenses in the point and shoots, but their picture quality, especially at any higher magnification is terrible compared to a good glass DSLR lens. Common sense should tell you that a $1500 DSLR lens that weighs a couple pounds is going to give you better pics than a usually plastic lens a fraction of the size and price will.
A quality DSLR set up will give you crisp landscapes, and is almost mandatory for good wildlife shots. In many situations, you can never have enough magnification for wildlife, especially birds. Todays DSLR's allow for quite a bit of cropping with little loss of quality. Try doing any serious cropping with a point and shoot...The results are usually pretty bad, and using the built in digital (not optical) zoom lens usually results in even worse results.
A Nikon shooter myself, if in your shoes, and looking for a very nice, mid priced set up that works for what you want, I would look at a D7500 (about $1200), a Nikon 200-500mm zoom (about $1300), and a Nikon 10-24 DX G lens (about $650). For the money, it would be just short of a full professional set up as far as performance, and the results would satisfy the most advanced amature.
And don't forget a good tripod (not a $39 special from Walmart) It makes all the difference in taking sharp photos, especially at magnification, where hand shake is magnified, even with the use of electronic vibration reduction. You'll notice the difference when a picture is cropped or enlarged / printed. The difference between a kind of blurry snap shots, and consistent razor sharp photographs makes all the difference to those who take their hobby seriously.
Larry