When you put a team together, it's important first and foremost to figure out how you're going to work together. Some mods prefer rigid role structures, while others are more collaborative. It's best to figure this out early before any kind of friction arises from incorrect assumptions.
The bigger the team the harder it is to coordinate, though of course running a zine takes a lot out of someone's schedule so being able to spread the work around is helpful too.
How you decide to differentiate roles is up to you. What I have below is just a list of basic skillsets and general responsibilities that at least one of your mods should be able to head.
Commonly conflated with graphics, but not quite the same. Do not ask for a graphics mod and assume they would know how to format a zine.
But someone needs to lay out the zine, make sure it has a Table of Contents, Credits page, title page, etc, that the fics (if you are including writers) have the right margins and are not just aesthetically pleasing but are readable too. They should also have access to and knowledge in working with publishing software that can do this kind of work -- InDesign is popular, but there are cheaper or free alternatives as well. (I've since purchased a one-time license for Affinity Publishing, which seems to be an excellent alternative.)
Commonly conflated with artists, but also not quite the same.
The person in charge of graphics should be able to set up a series of templates your zine will use in all advertising/promotional material. Headers, icons, announcements, countdowns, contributor features, and so on. You also want to do this in a way that gives your zine a distinct look or identity, that makes all of the graphic elements recognizable across the board. Strong graphics helps buyers feel confident about the quality of the product they will be receiving.
This can be divided between external communications (informational copy needed for websites, shops, applicant and buyer emails, answers to questions, social media posts, and other communications) and internal communications (contributor emails and Discord posts).
Either way there's a lot of this involved, and it's a little bit of an underrated skill. You can choose to decide how professional and personable your communication style is, but along with the quality of your graphics, your ability to communicate well says a lot about your level of professionalism, and may factor into whether or not people will choose to work with you or support your projects.
I wanted to separate this from Communications just because I think there is not enough attention paid to actually selling a zine, whether it's through keeping the zine top-of-mind during the creation period (when there's usually a dearth of external activity and chatter) or finding ways to remind people about the zine during the preorder period. It's pretty standard for zine sales to peak both at the start and end of a PO period, so figuring out how to encourage sales during the valley in the middle can only be helpful!
Sourcing quotes, negotiating prices, evaluating suppliers, and staying on top of your chosen suppliers are all part and parcel of supplier relations. Some mods already have pre-selected vendors only based on word of mouth, but it's important to do your due diligence in finding the best deals available for you as well! Some suppliers are known for cheap product but the quality is a little disappointing, so learn to check for samples prior to picking one supplier and sticking to it! You should also be able to check in frequently with them and not just trust they'll produce your orders in a timely fashion.
This pertains to the person who will be receiving, inspecting, and packing all your products for shipment. Depending on how well your zine goes this can be quite time-consuming so make sure you have someone who has the time to spare. It takes a lot of hours to go through each item that comes in (which is why I strongly encourage only a few merch items) and many more hours to package everything first in protective sleeves, and then in the mailers themselves (which is why I strongly, strongly encourage minimal bundle options too). This person should be detail-oriented, and ideally live somewhere with enough room and no allergens (like pets or smoke).
Your finance person isn't always the same person who is in charge of the Stripe/PayPal account, though if that's the case then they will need to work very closely with the person who is. But they need to be able to produce a working budget in order to help you plan ahead of what number of contributors to get, what kind of zine to produce, what merch items would come with it, help guide pricing strategies, and keep track of expenses as well as produce financial statements for contributor review after all is said and done. You would like someone who is detail-oriented and has a basic grasp of financial concepts.
There should always be one person whose job it is to think about the project as a whole, and thinking outside of their own responsibilities to ensure everyone else is on track too. (Sometimes this is everyone on the team, which is great, just be sure you're all on the same general page and can figure out how to resolve conflicting opinions. But projects start to fall apart when it is no one on the team.) It is their job to not only keep the team on schedule but also look ahead to what needs to be done, and make sure that those future tasks are getting covered ahead of time. There are a lot of different project management methods that exist out there, and a lot of different tools one can use to do this, but more important than that is the initiative to keep the project moving forward.
There's a lot of administrative tasks involved in running zines, primary of which involve managing contributor details, check-ins, and buyer orders. Someone should be able to keep track of this. You'd like someone savvy enough in Google Forms and Sheets who can manage data neatly and concisely.