Short answer: both are good!
Longer answer: Yes, you're allowed to cover songs and do not have to produce your own original song for this project. Though, in terms of fitting the story theme of the zine, some songs may fit the theme better (For example, Bokura no Kizuna somewhat fits the zine more than, say, Rakuen Oasis). If you want, you're allowed to reimagine any song whether it be using a different instrumental, adding to the instrumental, transposing, mashup, remix, mini medley, etc anything of that sort.
At the end of the day, every song tells a story so we have no rules against any songs specifically, though let's say it is encouraged that you add your own spin on songs you feel fit the zine less! Either way you can apply for the zine, we appreciate and welcome the talent of both cover artists and original song creators.