You can spot the four moons in modest binoculars, 7×50 or 10×50 being the best for this, and you’ll even be able to watch them weave around the planet night by night. If you have a small telescope where you can increase the magnification depending on which eyepiece you use, you’ll see the planet much more clearly and the moons will be more obvious.
Among the most interesting events to observe in the Solar System are the transits, occultations and shadow transits, where you can watch the shadow cast by a moon move across the surface of Jupiter’s disc. This can be accompanied by the transit of the moon itself before, during or after the passing of the shadow. In order to see this well, you’ll need at least a three-inch aperture (75mm) refractor telescope or a six-inch (150mm) reflector. A reasonable magnification of around 120x or even more is also required, as is a good quality eyepiece. Here, the Plössl design of eyepiece is good as it provides a nice wide and flat field of view with minimal distortions. Bear in mind that the quality of the atmosphere counts here too, so you may have to reduce the power if the air is particularly unstable causing a ‘wobbly’ image.
Longer focal length telescopes are better for planetary viewing, so this is where refracting telescopes also have an advantage, but again reflectors can also give you splendid views of the giant planet and its moons.