Fulfillment doesn't happen until the end of your preorder period, but you can make this part as easy or as hard as possible from the very beginning of your planning. And please, for the love of your shipping mod, please think about making it easier. A few ways to do this:
You should be ready to order all zine and merch items by the time POs close. You should be ready to order all zine and merch items by the time POs close. Maybe you are still waiting for hard proofs for things, and that's fine, but the end of the PO period is not the first time you should be figuring out how to put things together.
Most suppliers have templates and print guidelines available for use on their site. Provide these to your merch artists before they start working. (Some cases you may have to switch suppliers last minute, in which case it can't be helped. Be sure you can work with your merch artist through any necessary adjustments, but in a pinch it would help if you could make the adjustments yourself.) Print merchandise only usually needs a 0.125" bleed all around.
If you time this right, you should receive your products in 2-3 weeks and, after inspection, start packaging them up to send out.
Account for delays when ordering around peak seasons:
Basic product ordering guidelines
As you plan and budget for your zine, you should start thinking about what kind of protective packaging you'll need to take into account. For the zine itself, I think the most standard set of packing materials should be:
The first three can even be put together while you wait for merch and zines to arrive, so you're not wasting time during the production phase.
Flat merch would fit inside the zine itself. Consider putting uneven merch items like charms and pins in protective sleeves (if your charms are large, bubble pouches will help keep them from breaking in transit) and be sure to place them on the other side of the cardboard backing, so they won't press into and dent the cover of your zine.
Note: You might have noticed, but this is a lot of plastic, and is therefore not the most sustainable thing in the world. While suppliers like RoyalMailers are quite cheap, see if you can make your budget work with a more environmentally-friendly option like EcoEnclose.
When you have to ship out 50+ zine orders, it helps to have a shipping platform that can help you manage that volume as well as give you better pricing on shipping. ShipStation is a popular tool, but a co-mod (thank you, helwolves!) discovered PirateShip and I haven't looked back since.
Pirate Ship limitations:
It sounds too good to be true, but PS cuts out costs because they don't spend on advertising and rely on word of mouth. They are also set up by former Etsy sellers so they are catering specifically to small business users like zine runners.