Airsoft guns have the potential to propel BBs that travel with enough energy to shatter teeth, at least.
Your lips/cheeks do a bit to help, so keep your mouth shut, but they don't stop BBs.
If you get a lower face cover, go for something that's large, and goes over the ears, such as this:
As opposed to a small one, like this:
(I just google imaged those, so I'm not recommending you buy THAT EXACT ONE)
Those style masks are usually more comfortable, and have the added benefit of keeping BBs out of your ears.
The other big thing with the lower mask, is that it fits with your goggles. I bought a pair of goggles and face mask, and didn't even bother to try them on. I got home, and it turned out that the upper nose on the mask didn't fit into the nose area in the goggles.
With goggles, make sure it seals FULLY around the eye. If you get goggles that are too wide for your face, the strap might bend the goggles so they flex outwards at your nose, opening a gap at your nose allowing a BB to ricochet on up into your eye. This has happened to people (though it hasn't blinded anyone that I know of yet), and is pretty scary when it occurs. Wearing a helmet kind of helps keep your goggles seated nicely. If you plan to buy a helmet down the line, you should take that into consideration when you buy your goggles - large profile goggles will cause problems with your helmet (which sits low on your forehead) and mask alignment.
Paintball masks are simpler, because there's only a handful of companies that make popular ones, they're high quality, and well tested. Where as lower face masks can be complete crap, and not only let a BB right through, but explode little metal shards into your face (in a perfect storm type scenario). There's a lot of examples of BBs shattering PB mask plastic (their goggles are ANSI rated to at least the same spec as what's required for airsoft, so you don't have to worry about the goggles themselves shattering), or going through the little vents in certain PB mask types, but overall I'd trust them over a $25 Chinese mesh mask. (Not saying all mesh masks are crap though)