At some schools, any handheld meters have a habit of growing legs and walking away. A bench meter, even if it has mediocre specs, may be more suitable, simply because it's more likely to remain on the bench and not escape in someone's pocket. Something like an Instek GDM-8034 might be a reasonable choice for a lab.
Regarding Fluke's ruggedness and safety, they are legendary. However, most high school electronics courses can be done at low enough energy levels so that there's no danger of even the cheapest, worst meter dangerously exploding in a student's hand. If the experiments are done with low voltage current-limited supplies, either wall-warts, batteries, bench supplies, or similar, then a cheap meter may not present a huge danger to the students. There is a lot of learning that can happen with even a $20.00 multimeter, but as has been suggested, it should probably be considered a disposable item that will be replaced at least once per semester. Getting two or three per workstation would allow simultaneous measurements of voltage and current.
I'd say a basic lab bench for DC circuits needs at least a bench power supply with adjustable voltage and adjustable current limits, one or two multimeters, a breadboard, lots of test leads/stackable banana plug leads, and a number of passives, switches, LEDs, motors, transistors, etc.
For AC circuits, a signal generator and oscilloscope should be added. The frequency range/bandwidth isn't too critical for learning the fundamentals. In fact, keeping most experiments in a moderate frequency range can help in learning the basics without being distracted by parasitic effects that surface at higher frequencies.