Well, obviously hosting is going to be the obvious and easy choice both from a hardware as well as software and connectivity standpoint. Just about the only thing you will have to do in that case is design the content and load it.
From a hosting your own server/machine standpoint, that can vary a lot based on what the page is going to do and allow. Is this a static "announcement" page? Is it rich content that will be allowing animations and music? Will there be further prompts and links available to be followed such that all of the 1K users you project having access could be looking at and doing different things?
As to the bandwidth, since this is a school project that aspect will likely be more out of your hands and control than in. At the very least in a situation like that I would consider a "multi LAN" connection card or ability built in.
Spec wise I would consider that if the page is more static it's not going to take much CPU at all, with the requirement getting higher the more option and variable there is once landed. In both cases I would consider a great deal of RAM.
With a use case like this I would likely look to see what you could find on an older last gen blade/rack server if you were going to buy your own system to host from. I would go on the assumption that the schools IT dept will be helping you with configuring the IP/forwarding/etc for the local access needed.
I would also try to be clear with them what OS they are expecting you to have this available in. Server OS of the paid flavors can be high cost. There are Linux distros that are freeware.
As a sort of "for instance".
A few years ago when port forwarding services were still free and ISP would allow you control over your own port forwarding in a way they don't make as accessible now...
I created a Windows .mms server...a music server that myself and people with the address/password could connect to. At the time I made the system from the basis of a Pentium 4 computer. If I set the folder and put the music up to play at all times randomly I could have about 20 of my friends connect to it an listen without issue. When I set the folder to be a "player" type where the individual had choice over what tracks and order to listen in, that number went down to around 5. This was a problem not only of horsepower of the hosting machine, but bandwidth as well.