If an acrylic seems to be turning quite chippy, or when I'm working with some unbalanced wood on the lathe, I wear a face shield. I picked it up from Harbor Freight, and it's the cheap model.
When you first get it, it looks like it's got a bluish plastic for the shield, but that's a packing film to prevent scratching. Remove the thumb knobs on either side and disassemble the face shield .... peel the blue layer off. You will notice that the shield STILL doesn't look crystal clear. That's because the OTHER side still has a clear protective film on it too ... remove that as well, and then re-assemble your face shield.
Never ever ever use a cloth or rag of any kind at your lathe, unless you are rubbing some kind of finish or cleaning solution over the workpiece with the lathe powered OFF. If you are going to apply anything to a spinning workpiece, use a paper towel applicator, or a foam applicator ... not something that could potentially wrap around the spindle and grab your hands.
Keep flammables away from things that can spark. I know a lot of us use denatured alcohol or rubbing alcohol and many other finishing agents that are quite flammable. It should be remembered that ALL tool appliances with motors can spark, and in a flammable atmosphere, this can be a deadly lesson. Keep those containers sealed as much as possible ... only pull out what you intend to use, and remove it from the work environment as soon as is possible.
Dispose of used applicators, rags, towels, paper towels, ect in a fireproof container... preferably in a fireproof area of your shop, as well. Spontaneous combustion is NOT a workshop myth. Rebuilding a trash area is one thing ... re-building your shop, or in a worst case scenario, your entire house because it was attached to the shop.... That's a lesson someone only learns once. It's a good idea to learn from the mistakes of others before you make them yourself. Even more sinister is the possibility of losing friends and family due to your negligence in this singular area. Fire doesn't care who it consumes.
You only have one pair of lungs. It's pretty damned hard to get replacements. Use proper dust collection, air filtration, and a dust mask when working with extremely dusty items. Make damn sure you do it when you work with especially harmful items. Finding out that your WIFE is allergic to cocobolo by giving her a full-body rash every time you hug her is a surefire way to beg for a divorce. Setting aside a vacuum hose to vacuum yourself off before you head for the house is a good way to keep on her good side.
Your shop is only as safe as you can make it. Make it safer by installing a main breaker switch that will control all the outlets in your shop other than the lights. Switch it off when you're not going to be using your tools, and set it up so that it can't be switched back on without YOU there to supervise by either locking the box or hiding the breaker switch location so that your kids and their friends can't "play" with "daddy's toys". Heartbreak is defined as finding out exactly what it's like to bury your child.