What's your budget?
1a) If you're really wanting to pick it up as a long-term hobby, a gently used starter DSLR with the kit lens and an inexpensive "prime" lens will be a good kit. For instance, a Canon T2i or T3i, the 18-55 kit lens, and an inexpensive prime such as the 50mm f/1.8 (aka "nifty fifty"). I'm sure there are Nikon equivalents that will be about the same price and capability.
1b) If you just want to take pretty-good snapshots, but you don't really want to explore photography as a long-term hobby, some of the newer mirrorless or bridge cameras will be a better idea. If you use a DSLR but you leave it on "green box" mode all the time, and don't bother learning some of the settings, the photos will be no better than a decent point-n-shoot or bridge camera.
"Bridge" cameras are so named because they bridge the gap between a compact point-n-shoot and a full DSLR.
2) That's a question that's hard to answer briefly. At the most basic level, the lens has two primary attributes:
2a) Focal length (or magnification, or reach), and aperture (or f/stop). Most starter or kit lenses are "zoom" means they have a range of focal lengths, such as 18-55 which means 18mm (pretty wide angle) to 55mm (moderate telephoto). Then there are "prime" lenses, which don't zoom (e.g. fixed at 50mm), but primes almost always have a wider aperture and/or better quality glass elements.
2b) Aperture, in short, is the size of the opening in the lens where light passes through to reach the camera's sensor (or film). A wider aperture, denoted by a smaller number (e.g. f/1.4), will let in more light, and give you a shallower depth of field- you know, that effect where the subject is in focus but the background is blurred. A smaller aperture, denoted by a larger number (e.g. f/16) will let in less light and give more depth-of-field.
2c) A variety of other attributes that can be argued and nitpicked all day and all night. Sharpness, bokeh, minimum focal distance, focus speed & accuracy, build quality, .... and so on.
3) As with most skills, the more effort you put into learning your craft, the better your results will be. A fancy and expensive camera does not automagically make great pictures.
Rule to live by: Look for the light. Once you start to see light and shadows, you'll start to make better photos.