There are two main designs of coffee grinders, each with advantages and disadvantages…
Blade grinder; like a miniature food processor/blender, has a blade at the bottom that spins to cut and grind the beans
Pros;
generally inexpensive
compact
somewhat quiet
you can somewhat control the size of the grind by how long you grind the beans, quick grinds yield coarse particles, longer grinds yield finer grinds
easy to clean
Cons;
inconsistent grind size, coffee particles in a grind can vary greatly between coarse and superfine
running it too long can “burn” the beans due to friction
when grinding, since it doesn’t eject the grounds into a collection cup like a burr grinder (detailed below) some previously ground beans get re-ground and re-ground
small capacity (3 cups maximum on average)
the Burr grinder uses two “stone” wheels facing each other, one fixed to the underside of the coffee hopper and facing downward, the other mounted to the grinder motor spindle, as the bottom stone spins, it grinds the beans to a certain size and ejects them into a collection cup
Pros;
consistent grind size, no over or undergrinding
grind size can be varied from extra fine to coarse, and the grind is, as stated above, consistent in size
no over-grinding or “burning” of beans
Cons;
more expensive than a blade grinder
noisier
takes up more tabletop space
harder to clean
coffee afficionados generally prefer burr grinders, and tend to look down on blade grinders, i see coffee as nothing more than a hyper-efficient caffiene delivery vehicle, so grinder type is less of an issue with me, that said, i do have a burr grinder, as it’s just generally cooler 
the grinder isn’t as big a factor to non-afficionados, the best steps for great coffee are to use freshly roasted beans, clean water, and a clean coffeemaker or french press
i’m no coffee expert, but i know what i like, a nice microroasted whole bean coffee, but any whole bean coffee is good, preground stuff is more convenient, but ages quicker once the package is open, i grind it myself moments before brewing it in my little French Press pot