Quite a number of comets have been discovered with the naked eye, or discovered after they were of naked eye brightness. So, what you are doing by adding additional equipment to your eye is simply improving your odds. There are a zillion different types of telescopes, and range from as little as a couple hundred dollars to many, many thousands. They come in all sizes and configurations, and when you begin to take accessories into account, the options become absolutly dizzying. But we can narrow our choices by examining what we know about the physics of comets.
Comets begin to form a coma as a result of sublimated gasses as the nucleus nears the sun.
Near is relative for a comet. At this point the comet becomes non-stellar, that is it no longer appears as a point light source like a star but rather has a measurable size, similar to a globular cluster or galaxy. We need to take one other detour before again discussing telescope specifics, and that is in magnitude. A comet's magnitude, or apparent brightness, is defined by comparing its brightness to that of a defocused star. Actually, its more complicated than that, but basically what the magnitude of a comet says is that if it were stellar, its entire size compressed to a point light source, that's what is magnitude will be.