Don't know about "highest quality brand" on the market, because it's pretty much a given that if you want a quality mouthguard, the best thing to do is to hit up an Orthodontist/Dentist and pony up a couple hundred dollars for a fully custom-fit one (especially if you have orthodontic devices like braces).
Other than that, most MMAist and grapplers will use single pieces. From a plain/generic single, all the way up to the more price Brain Pads, you want to get one if you're in any type of contact sport. Myself, I've broken 2 molars grappling, but suprisingly never had any issues during stand up. In either case, even if I had a $2 generic from Big 5, it wouldn't have happened. You will probably only worry about a double if you are doing a lot of dedicated striking.
In either case, if you are thinking about competing you want to get one ASAP. Having a mouthguard in place changes the way you breathe pretty dramatically and you want to get used to that. I actually have 3 mouthguards myself (2 plain generic ones for regular training and drills, 1 Shock Doctor Pro for sparring). You can look at this page
here to get an idea of what's out there.
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