In their native habitat, coffee plants grow into medium-sized trees. But growers regularly prune the plants to be a more manageable size, especially when the plants are grown indoors.
(Note that you can't grow coffee plants from the beans you buy in a store; those have been treated and roasted and will not sprout.)
Even though coffee plants are vigorous growers, it will typically take a few years before your plant produces flowers and subsequent fruits. All parts of the plant are toxic to pets and humans—the beans are edible to humans.