Headgear:
There are many different types of headgear out there to choose from. It will come down to personal preference what one you choose. The biggest complaint athletes have is that they loose some peripheral vision when using bigger more impact resistant headgears. This can lead to them misreading punches and getting hit more often. The bigger headgear also makes you a bigger target and requires you to move more to make punches miss.
On the other end of that, a smaller headgear may give you more vision and make you a smaller target, but will provide less protection when hit. The biggest thing I see as a coach that headgear helps protect from is getting cuts after accidental headbuts and elbows. I do not belive that they help prevent concussions, but do help stop fractures in the cheeks, eyes, broken noses, and black eyes. Some headgear has a bar going across the nose to prevent getting broken/bloody noses. This headgear make you suseptiable to uppercuts that will knock your headgear upward. The boxers that I see use this the most are ones who get bloody noses easily.
Some headgear have cheek protection, while other ones are open faced. Some have velcro straps, laces, or hook and loop fasteners like a belt buckle. It will all come down to personal preference.
Why do I make my boxers wear headgear when they spar? They make you wear it in the match. When I coached MMA and Kickboxing, they were not required to wear headgear, so I did not require them to wear it when sparring.
USA Boxing does have specific competition headgear you must have for your match. A "USA Boxing Approved" tag must be on the headgear. (Tag shown in picture above). There are many different brands that make this kind of headgear. The most popular being "Sting", "Fighting", "Title", and "Ringside". They range between $100 and $160 dollars.
In big tournaments if you are in the blue corner you can not have on red headgear. If you are in the red corner you cannot have on blue headgear. So I always suggest getting a neutral color, black or white, so you don't need both.