When are private lessons worth it?

Not at the start. Private lessons are the most expensive way to learn things a group class teaches fine: footwork, distance, basic bladework. The consensus among coaches is to wait until a fencer has about six months to a year of group classes, genuinely loves the sport, and has started bouting, that's when individual attention starts compounding.

The moment privates clearly pay off is when the fencer starts competing. A lesson then isn't 'more fencing', it's a coach fixing the two or three specific habits that are costing them touches, which no group class has time to do.

Frequency: one 20-30 minute lesson a week is plenty alongside classes. Twice a week is competitive-teen territory.

Cost varies widely by coach and city, ask the club, and don't be shy about it; every club is used to the question. If the budget is tight, know that many successful fencers take a lesson every other week, or only in the two months before a big event. And if your child is at a club where a beginner is being pushed toward mandatory private lessons in month one, that's a sales pitch, not a training plan, reasonable clubs don't do that.