If your kid is just starting fencing, the mask is the only piece of gear you cannot get wrong. Everything else — jacket, glove, weapon — has a margin for fit and growth. The mask doesn't. A loose mask can slip mid-bout. A too-small mask is uncomfortable enough that kids won't fence in it.
Three things to look for
First: the safety rating. US Fencing requires masks to be 350 Newton minimum for sanctioned competition. For practice in any reputable club, that's the floor. 800N FIE-rated masks exist, but you don't need them until your child is competing at national or international level — usually high school age.
Second: fit. Masks come in S, M, L. Try one on before you buy if you can. The mask should sit firmly on the chin and brow with no rocking when the fencer turns their head. The bib (the fabric flap that protects the throat) should be long enough to tuck inside the jacket.
Third: the bib. The throat protection piece is the part of the mask that fails first. Look for a bib with at least double-stitched edges. Some cheaper masks have bibs that delaminate after a season.
What to avoid
Don't buy used masks unless you can inspect the mesh personally. Punch tests reveal weak points, and a mask that's been hit hard can have invisible fatigue. Don't buy plastic masks for anything beyond casual play — they're for PE class only, not real bouting. And don't size up assuming your child will grow into it. Wrong sizing in masks is dangerous.
Tim's pick for first masks
At our clubs, we start kids on a 350N foil mask regardless of weapon, because the geometry is forgiving and the price is reasonable ($95). Once they're committed and competing, we move them to weapon-specific masks (sabre has electric scoring, épée has whole-body target — different masks, different cords).