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I don't keep them on a shelf, I keep them in a bag that I got on Amazon that's fantastic for carrying games around. My collection is still fairly small and I travel around a lot so I just take them with me. I tend to keep them in there horizontally as well.
Holy cow you have a lot of games. And I seem to get maybe five or six plays before the corners start to tear, it sounds like maybe I am being rough. All I do is grab the top of the box by the sides and shake it so that the bottom will come out, I always tried to be gentle but maybe that in and of itself is being rough. And I keep them in a bag I got on Amazon and transport them all the time.
I bought this cargo duffel bag from Amazon for ~$20 and love it. It holds a lot of games, is square shaped so they fit snugly when stacked, and has handles and an optional shoulder strap.
you could try a duffle bag. this one is about 36" long by 24" high by 15" wide. it should easily fit your pc and other gear. there are plenty of other duffle bags out there, but this one was one of the first i found.
This bag. It holds 6 games flat and some smaller ones on the side if you don't mind putting them in sideways!
I use this canvas cargo bag. It holds quite a bit, so it might be overkill if you're just carrying a few games.
Rothco Canvas Bag
Fits about 6-8 "normal" sized square boxes. I've put lots of games and weight into this bag over the years, still good as new.
I ordered one of these from Amazon specifically to transport the core box for KDM 1.5:
It didn't fit. Or more appropriately, it would only fit at a weird angle, with much stretching, and was very difficult to get back out.
I have a couple of these for hauling games around to various game nights. Holds about 7-8 ticket to ride size boxes with room to spare.
get a Rothco Parachute Canvas Bag (price in Amazon link)