I used to clean my arrow-shafts with acetone before I applied glue. However, I was told that I should be more careful with it, because of its toxic vapors and stuff.
Which breathing mask is recommended? Should I wear glasses and/or gloves?
Acetone is often used in nail polish removers, if it's at this strength no you would not need a mask, just make sure you're in a well ventilated room.
For high percentage acetone cleaners used to remove resins and such, you should think about wearing a ventilation mask, gloves, and also possibly goggles to protect your eyes - in addition to being in a well ventilated area.
If it stings your eyes you're probably working too close, but glasses wouldn't help (goggles might). If you're using it a lot you may find it dries your skin so you could choose to wear gloves (or avoid getting so much on your hands).
From using acetone a lot in industry and academia I can tell you that people use it freely without ill effects all the time.
If you're soaking stuff in it, use a lid as it evaporates fast. It's also flammable.
Acetone smells scary but is really one of the less dangerous chemicals used for dissolving stuff. Main nasty effects:
I advise to do your job in outside or in ventilated area and wear gloves if you don't want to have dry skin. If you feel dry skin just use hand cream.
You should work in place with good lighting so that you don't watch your work closely - that would cause you to inhale more and generally increase exposure.
Don't smoke, don't apply on hot surfaces or on-line electrical devices (eg. in effort to clean connectors).
If you feel dizzy or tired cease your work and go for some fresh air. Seal the container properly before doing so though!
Unless you are exposed constantly, you can probably deal with this by setting up reasonable ventilation. Either work outside, and stand crossways to the wind, or set up an exhaust hood or fan to pull air from where you work to the outside.