I wasn't sure if cage head gear was exactly how it sounded so I googled it...it is exactly how it sounds. I don't know what your gym is like but as golden boy said you would be laughed at a fair bit in my gym. As well as looking a plank, you look like you should be fencing (the sword kind not the around your garden kind) Get a green hill one, mines pretty good. Not too expensive either. Might as well wear one similar to the one you'll be competing in, get used to getting hit.
a lot of boxers are recommending this gear since its similar to the expensive japanese brand. weird name though. http://www.ringtocage.com/Deluxe-Full-Face-GelTech-Sparring-Headgear-RC50FS.htm
How about before you ask stupid questions you go to a gym or watch one on tv and count how many cage headgears you see.
Cage is probably best, but I think there is a case for "too much" protection. A defining point of Boxing is getting used to getting hit. There are certain anatomic and employment points where a man needs better nose protection, but if you can get away with it? Less is more. So if you must have 100% face coverage? Get a face bar. If you need 110%? Get a cage, but also be man enough to buy two so that anyone who spars you is covered also. The catch is that a rigid plastic cage transfers shock almost too well. A good shot placed on the cage could turn your head gear or buzz you. Neither of which would be as realistic as glove on skin. Get the bar, or better get Mexican style with the chin guard.