A display and a PC is just a part—and not the most important nor expensive—of the whole setup.¹ In order to minimize costs, you should consider the following aspects first:
How should the devices—whatever they would be—would be powered? Since the setup is in a school, there are strict rules related to the safety of electrical installations.
There probably needs to be cables inside the walls going to where the monitors will be installed. How would monitors physically connect to those cables inside walls? Should there be a dedicated outlet near every monitor? What the laws say on the subject? How much would the school pay an electrician to do the job for every classroom?
Places with high presence of children are not the most friendly one for fragile hardware. You should essentially ensure all the hardware is protected against vandalism: this includes intentional vandalism by a child who wants to break things, as well as theft or accidents (for instance a children pushing another one against the monitor during a fight).
This should not only influence the choice of the hardware, but also the way you connect it. For instance, why asking parents to buy a Micro-USB cable when there are lots of them to take by unplugging a Raspberry Pi?
Infosec. Children may not only be violent and malicious towards hardware, but some of them are quite skillful at breaking things at software level. This means that whatever your setup, it should be updated on regular basis and be protected against basic attacks.
Not a big deal? Wait until your dozens or hundreds of Raspberry Pis start a DDOS attack on school's LDAP server. What about explaining that to the headmaster?
Maintenance. Installing the devices is one thing, but how much would it cost to maintain the system over the years? Some setups would have a high original cost, but would make maintenance as easy as possible. Other setups would be much cheaper originally, but incur high maintenance costs.
Based on the first three factors, I would claim that Raspberry Pi coupled with an HDMI monitor is not a solution:
It's difficult to make the electrical installation which would be compliant with all the safety rules (especially for a school). The fact that you need either a transformer or an USB charger is, alone, a big issue. Both transformers and chargers have a big issue: heat. This means you cannot put them inside the wall. You won't be able to put them outside either, because of...
Vandalism. How do you imagine protecting a Raspberry Pi against the attempts of stealing or disassembling it, or simply trying to destroy it? Even if you put it near the ceiling, children will find a solution to do nasty things to it.
Raspberry Pi devices are much, much better compared to IOT devices such as smart light bulbs which have practically no way of fighting against a determined hacker. Raspberry Pi has several great things: (1) it runs Linux, (2) it has enough power to do cryptography and (3) it supports 802.1x EAP if you use Wi-Fi.
If administered correctly (updated regularly, configured wisely and monitored by a system administrator), they are not that different from, say, servers: the only differences are that servers have two or four NIC which makes it possible to have a dedicated network for system administrators (important when you're being DDOS'ed), and that some servers are much more powerful, making some DOS/DDOS more difficult.
The problem is, Raspberry Pi devices are not usually considered as servers by system administrators, which means that they are not actively monitored, not configured by skillful personnel, and sometimes end up completely forgotten, with outdated kernel and software. Lots of such devices in hands of a hacker can do a lot of harm.
Your solutions are therefore those ones:
Kiosk. Essentially, electronics (monitor and PC) are embedded in an enclosure or are inside a wall, and the hardware is specifically designed to be this way (with fans where appropriate).
Benefits: (1) safety is not an issue, since all the wiring is inside the enclosure; (2) all kiosks are designed to be protected against different degrees of vandalism and many companies would advertise their products as safe against hackers (there is often a difference between what's advertised and the reality, however).
Drawbacks: (1) most hardware is quite expensive, and (2) most devices use touchscreens: it's expensive, and you probably don't need it.
A variant of a kiosk is an enclosure with a tablet in it. Might be nice for a hotel lobby (although every time I've seen one, it was terribly done), but not for a school.
A monitor with an embedded PC in it, mounted on a VESA near the ceiling. This is essentially what is used in public locations: supermarkets, airports, railway stations.² Those are not just monitors, but devices which look like monitors but which have a PC built in.
Those devices can potentially be vandalized (as would any ordinary PC monitor, for example) and the wiring is outside the device (just like in an ordinary PC monitor). The idea is that those devices are installed near the ceiling, in a location where there are lots of cameras, people and security officers, so a malicious person (a vandal who wants to break the device, or a hacker who wants to connect something to it) won't be able to pass unnoticed if he starts climbing to access the device.
Benefits: (1) much cheaper compared to kiosks, and those are never touchscreens. (2) Since those devices are expected to be found in public locations, companies that sell them will claim different degrees of protection against hackers. As in previous one, it happens that a seller would claim something which is not true.
Drawbacks: (1) check the local rules to be sure such installations are authorized in a school; (2) you have to install them near the ceiling.
Custom-made everything. Essentially, you pick your hardware and you design the enclosure (for instance by relying on a laser-cutting service).
Benefit: you can pick inexpensive monitors such as the ones produced by Waveshare, including their e-Paper modules (given the sort of information you want to display, e-Paper modules may be a much better option compared to an ordinary LCD screen, and they consume much less energy).
Drawbacks: (1) you have to know how to do the stuff, and it takes a lot of time. (2) Check the local law in terms of what you can or can't do in a school. (3) Beware of maintenance complexity and cost. Replacing a custom-made metal laser-cut part is quite different from replacing a device that you can simply buy on Amazon and have to be delivered the next day.
¹ I had a similar experience recently. My goal is to have a touchscreen near the door in my flat, in order to deactivate a custom-made alarm system which triggers when someone opens the door. So much simpler than your project, since I'm doing it at home, and not for a hostile environment. Buying a screen module and a Raspberry Pi was easy. The difficult part was all the wiring, as well as the task of putting the transformer in a way it won't heat and the ability to do maintenance easily (including cleaning dust). In addition to that, I had to make custom enclosures, which costed me a few hundreds of dollars (in part because of the mistakes I did), and I wasted about a week designing them. And the next difficulty would be to develop the software and ensure the operations part.
² At least, one of the types of devices they use. What you find a lot at railway stations and airports is a different kind of device: special monitors which have special connectors (like the CCTV you can see in railway stations). Those devices are more common in locations where vandalism is relatively easy (for instance a suburb railway station where there are CCTV, but no security officers on premises). Unfortunately, I couldn't figure out if those devices are just monitors or hybrids (monitors with a PC inside). If I remember well, there are two heavy-duty connectors: 230V and something used for communication, but the communication one doesn't look at all like Ethernet or HDMI.
