Need advice to setup university WiFi in rural Uganda

Hi! First time poster here. Not sure if this is the right sub for this question - if there is a better place to post this please let me know.

So, the gist of it: I'm a computer scientist involved in a (social science) project to bring video-based e-learning to a remote university in Gulu, Northern Uganda.

We want to offer the students of this university access to world class online video lectures, such as those from Stanford or other institutions. Many of these videos or courses are available online for free. The problem is that there's no inexpensive or reliable way for the students to get to these videos.

There is (glass fiber!) internet at the university, but it ends in the "server room" (if you can call it that). There is no WiFi network. There are three or four computer labs with about 400 decaying Pentium 4's in total, all of which are running some ancient version of Windows. The university does not get all the potential bandwidth from the fiber connection (which was installed by Google), but they are paying for something like 20Mbit. They are considering to increase it to 30Mbit or 40Mbit. Perhaps unsurprisingly, the university administration itself has decent computers and good internet. Students typically have cheap Android phones, and they all have 3G (or 4G?) internet through a mobile provider, for which they obviously pay out of pocket.

Within the university it's easiest to sell this project by using the flipped classroom approach: the video lectures don't replace the regular lectures, but they're given as homework.

So, how do you get video lectures to these students?

- They cannot use the decaying computers (because they're decaying and because you can only use them while on campus, and not at home as homework). Also, it's unclear if the university's limited internet connection would be enough for this.

- They typically don't have laptops or computers themselves, so that's out of the question too

- You can't ask them to watch these lectures on their phone, because they would have to download them using their mobile data bundle, and that's really expensive (especially for large video files) so you can't just demand that from them.

So, the plan I came up with is to install a local mirror server that will download and host the video files, so that the university's internet connection only has to download the video once. Then, I want to install a proper WiFi network on campus so that students can connect to the university WiFi with their phones and download the video from the local video mirror server. I will probably have to develop a small app for that. Then, students can take the downloaded video file home at watch it as homework. Could work, no?

However, I'm a programmer and not a network engineer, and I have no fucking clue where to start. I will go there in early May for one week and would be able to bring and install some hardware.

The WiFi routers would be installed outside, in a humid and hot climate. I think it’s possible to shelter them from the rain, if necessary. We have to assume the power can go out at any time (regular power cuts), and we cannot make assumptions about the skill level of the people who will end up maintaining them - so it needs to be as fool proof as possible. The routers itself can/will be connected to ethernet. Additionally there’s a limitation as to how many devices we can take into the country: about 10 or so. Ideally we'd cover the whole campus, but if it's better (or more realistic) to only cover a part, that's fine. On good days there would be a few hundred students on campus at the same time (300 or 400 or so).

Our budget for this is about €5000…. Do you think it’s possible? Feasible, even?

I'm grateful for any input you might have. If you think it's ridiculous, please say so. Do I need a higher budget? How would you approach this problem?