I work in schools. I've done their IT for something like 15 years now.
The schools won't care about client storage. You either store on a server, or you store in the cloud nowadays. And you're hardly storing anything anyway. The sum total work of a YEAR of kids will likely be a few Gigabyte unless you're storing lots of video - and the video you store will be all the intermediate work and not their final product.
The magic words are "VLE". Everything is done with web interfaces and portals anyway, interfacing into user areas. Other schools use Google Apps for Education (which gives you UNLIMITED online storage for email and for Drive if you're a school). Most schools will have redundant broadband as an absolute minimum and leased line as standard. A lot of them host their own website in-house, for services like the VLE, OWA, etc.
Yeah, sure, the net goes down sometimes, but it's not "business-critical" in that sense. You can do a few days without it just by saving locally, using the VLE internally, etc. but some of your outside services might suffer. And on leased line, a couple of days is the only outage you really see and you'll have broadband (or even 4G) backup for that. I've run a private school with 100s of machines, tablets and users from a bunch of 4G SIMs when our dual-ADSL2+ broadband contract was severed against our will. We got in another broadband line within the week and leased line in replacement within a couple of months.
You know all those "bring your iPads to school" kind of places? How do you think they are operating? The cheap Wifi-only iPads (don't want to give the KIDS 3G because it has no decent filtering) are 16Gb and most of that can be used up with apps and the OS upgrades. They use the cloud offerings and the VLE etc.
Your ability to teach is not hampered while the internal network keeps running. Your external services (submitting homework via Google Drive, or downloading the question sheet from your VLE) may be somewhat hampered but it doesn't take a lot to make them accessible from the world in an emergency.
Hell, most places use software like ClarionCall (web-based messaging service for emergency emails/texts or even just sending the newsletter home), some use Office 365, a lot use Google Drive, remote-desktop, VPN, etc. It's not actually that crucial at all to have local storage.
In fact, my deployment image - with every piece of software and every driver for every PC and laptop in school - is about 45Gb. And on most clients most of that is unused. The biggest things you'll ever deal with are roaming profiles but if you're deploying Surfaces and Chromebooks, etc. they have an entirely different use case anyway.
There's no reason to need a lot of local storage in a school, or even a lot of RAM. The last year of so is the first school I've worked at that guaranteed 4Gb of RAM in every PC. And we run Windows 8. Properly managed, it's just not a problem even with a "login surge" every hour as one class logs out of every PC and the next class comes in and logs into every PC.
And the amount of stuff you have to actually keep? Well, you submit that to the VLE from your Google Docs or whatever, and it gets stored in the server and backed up with your normal file storage. You aren't losing anything and don't need independent storage for everything.
In fact, in my school, my first action was to ban USB keys. Rarely used, unreliable when heavily bashed about, a virus- and data-transferrence risk, and the cloud offerings we have do a better job for zero cost (I'm not issuing encrypted USB sticks to every member of staff just so they can take work home, and certainly not to every pupil).
In computing everything comes in cycles, thin-client, fat-client, centralised, decentralised, etc. At the end of the day you use both and all in everything you do. Thin-clients logging into VM's or using cloud offerings alongside fat clients for "real" work with access to the same data.
Site-wide wireless is the norm.
Tons of on-site servers, storage and services is the norm.
Redundant / resilient / leased lines are the norm.
VoIP and even SIP is the norm.
Cloud / Private Cloud (VLE) accounts are the norm.
The pupils are more than welcome to take their own backups but, you know what, when all your stuff is mirrored to all the possibilities anyway, they never need to. Google Apps for Educations offers not only AD authentication sync but even storage sync and EU-data protection guarantees (a billion times more than Apple does). And if you think on that as "working" space, but then have an official portal to submit "recorded" work (homework, coursework, etc.) it really doesn't matter if the cloud goes down or the Internet goes off.