When you say assignment, do you mean this is course homework? That might be putting people off answering…
Either way I can’t really help much, but I thought the usual thing to do with these sort of machines was to setup ltsp with a read only thin client image stored on the server. That way you are not restricted to 1gb storage space.
1gb is not much in Ubuntu, even for a cli only install it will be a struggle.
If you really have to create an image to be installed on the client, then using a lubuntu live ISO as a starting point would be a possibility. The compression used reduces the space needed to below 1gb.