When I did my first Year of Zines in 2015, I started out with free word processing software and a $99 black-and-white laser printer. By the end of the year, I was making each zine by hand with copy paper and a black Sharpie pen. Sounds backwards, right?
All of which is to say: you do you. I love both digital and analogue, and most of my work falls somewhere in the middle. How you make your zines is completely up to you. What equipment do you have on hand? What practices do you enjoy most? If you're a '90s kid like me, maybe the answer is a little bit of both paper and pixels.
Here is the equipment I have on hand right now, all of which I can recommend after years of use (and multiple purchases of the same thing; ask me about my three Brother printers some day).
Brother HL-L2370DW Wireless Monochrome Laser Printer
Brother HL-L2390DW Wireless Monochrome Reliable Laser Printer
Swingline Long Reach Anti-Jam Stapler (SWI34121)
Sharpie Fine Tip Permanent Markers, Black, 5 Pack
Fiskars 12" Portable Paper Trimmer
Canon CanoScan LiDE400 Image Scanner
Trodat 4810 Printy Self-Inking Line Dater, English
Trodat Do-It-Yourself Printy 4911 Climate-Neutral Self-Inking Stamping Kit, 3-Line
Staedtler Mars Lumo Graphite Pencil - B 4B (100B-4B)
Westcott 24"x36" Double Sided Cutting Mat, Blue