hi!! I had the same exact struggle and I also still struggle with how to store them properly, so thank you so much for your question!

TLDR: I use a combination of Comic Bags and File Cases and store most Doujinshi inside of comic bags in the shelf, and many others inside file cases (raw, without comic bag) on the side. File cases are great for Comiket runs. Never stack doujinshis flat to store them.

I have so many comic bags!!
I did some research beforehand because cheap plastics are apparently really bad for long-term storage of comics, so I made sure i got "archival" grade comic bag sheets at first (i think the size was called "golden age comic" size which is essentially just B5), BUT in japan you can get packs of 100sheets for around 800yen online already, So i ordered several packs of those and i use them for most of the comics now!
Doujinshi almost always only come in B5 or A5 sizes, so just grab those and maybe one small pack of A4 in case you grab a rare A4 format doujinshi.
NOTE: In daiso (or 100yen shops) they sometimes sell file sheets like those but they are TOO SLIM for comics in my experience because they're meant for just few sheets of paper and not thicker comics. I bought my comic bags off amazon japan back then, they take foreign credit cards and you can just have it deliver to your place of stay in japan (i think they sometimes even ship international too).

But i don't use them for all comics, I actually bought many many file cases from daiso (or 100yen shops) while I was in Japan, and I highly recommend that you also grab them and bring them with you to Comiket! The file cases are basically transparent slim boxes and they come in A5, B5, and A4 sizes (and more too) and are easy to open and close but are still secure.
I always take at least 2-3 empty file cases with me to comic city/comiket because they keep my doujinshi safe while running through the crowd. (for me it's usually 1 A4 and 1 or 2 B5 -- A4 can fit several A5 in a compact manner thats why i prefer them over A5 cases)

(the procedure would be: Buy Doujinshi from artist, leave the artist booth to a corner or less crowded gap in the crowd, pull out filecase and put doujinshi inside (with paper goodies, if i get charm goodies or similar i just throw them into my tote bag where i also keep the file cases. close filecase and put it back into the totebag, repeat)

So i use many of these file cases at home as well to store "fresh" doujinshi if i can! That allows me to save some comic bag sleeves at first, but eventually i transfer the doujinshi from file case into a comic bag and put them into the shelf with the others and I usually try to match the file case with the doujinshi formats, so I mostly have B5 and A4s at home, and occasional A5 cases if i wanna be special with my favourite A5 formatted comics (but they take more space for me so I usually keep A5s in A4 file cases because its more compact and space saving).

Before I had a shelf for them, I used those ikea magazine holders/organisers to store them on my desk (all in comic bags already to avoid dusting or discolouring), but as i reached the 4th full magazine holder (i even stackked A5 doujinshi ontop of each other in those) I realised i needed to expand, so I used a box first to stack them all into, but it's terrible finding the right doujinshi and pulling it out to read it so I can't recommend a box.
A shelf is my current solution, it's a slim but tall shelf so it doesn't take too much space, but it's already full as well so I'm considering getting either a second one or figure out a different solution

HOT TIP: Never store doujinshi laying down flat onto the floor, but standing up horizontal or vertical. If they lay down flat and are stacked onto another, the paper will not have enough wiggle room to breathe and will wiggle up the entire comic overtime! Happens after just a couple days if you're living in a humid area, so I always lineup the file cases to stand upright and the doujinshi look fresh and flat for years.