There are a lot of ballgag types these days, but I wanted to show this particular version as I would certainly recommend it if you had to only have one ballgag and a good choice in general.

The classic ballgag is pretty much some sort of ball with a leather buckling strap going through it. Some mix it up with extra O rings on the sides or an extra strap like a chinstrap, but generally all are the same concept until you get into more specialized variants like head harness versions. Since simple, the small details matter like the ball and strap quality. Preferably there are no extra mold seams on the ball and a little squish is nice as opposed to something fully rigid like a metal ball which can be a bit harsh on one's teeth. 

This Deluxe Coated BallGag covers those keypoints well where although you can vaguely see where a ball seam may exist, the coating smooths it out quite a bit where it is not noticeable in one's mouth. The coating also seals the ball connection points which usually are a pain to clean on classic ballgags. Since fairly thin but rounded, the side connecting straps also are more gentle on the lips and sides of one's mouth compared to typical wider leather straps. For those curious about the coating, they claim it to be a Synthetic Rubber (latex free). The main neck strap is fairly straight forward, however is a locking buckle setup which is always a nice feature when possible.

As a plus they offer 3 sizes, but I find the currently shown medium at 1.75" ball diameter to be the best. The small at 1.5" is certainly an option for those with jaw issues, however generally will not fill the mouth much even in small females. The large being 2" is more for those who really want the mouth filled and pushed wide open, typically this size will cause rapid jaw soreness on most people though. Thus medium is a nice middle point allowing the correct behind the teeth placement and filling the mouth to prevent speech while not being so overkill you have to take it off in 5 minutes. Although I show the black version, the classic red ball zone version is also available.

For advice on putting on any ballgag, I recommend first putting the ball in their mouth, making sure it goes behind their teeth. This can be done in many ways, but most end up going under the lower teeth first, then slipping under / past the top teeth. Once in, have the bottom look down to be able to fasten the buckle on tight. This way the strap doesn't end up floppy and loose when the bottom looks down or moves their head in other positions.

At around $50+ The Deluxe Coated BallGag isn't cheap, but the gear snob in me appreciates the finer features that make it the best one I currently know of. I'm not sure of the manufacturer as there is only a faint MB logo on the side of the strap so currently I only know to purchase them at MR-S Leather. There are similar variants for cheaper such as the Hush Comfort Silicone Ball Gag, but the ball area is made differently and has noticeable mold seams.

http://www.mr-s-leather.com/HT065/deluxe-ball-gag.html

One that appears similar, but I have not been able to confirm in person: 
http://black-rabbit.com.au/shop/bondage-gear/gags-and-bits/super-grip-locking-ball-gag/

Copy variant example (made differently / has mold lines):
https://www.extremerestraints.com/ball-gags_150/hush-comfort-silicone-ball-gag_8720.html