I’ve previously used birdcages (I hate the large handle on top that restricts storage), versa (I like the slim and durable construction of these), and traditional aluminum cases (cheap and not at all confident carrying these around).
Not sure if anyone’s recommended these in the past (I’m new here!), but I currently use a Fomito AB-27 camera bag (interior dimensions 41cm w x 28cm d x 22cm h). It’s about $50 on Amazon and can hold up to 15 racks. I’ve got mine set up for 12 racks (4 across x 3 high) with room for a couple card set-ups and dealer buttons. The case comes with Velcro partitions so you can customize, but as you can see, I use most of the partitions as cushion and filler. The base can actually fit five racks across if you need to fit a few more than I do. There are a couple of mesh pockets on the side walls perfect for extra cut cards, buttons, or card protectors. Since it’s fabric, it’s not as sturdy as the other options out there, but it seems solid enough for my needs. Single handle on top, but also a shoulder strap, which makes all the difference. For me, that means up and down a few stairs, in and out of the car, to and from home.
It sits a little cleaner on a shelf than a birdcage (shelf big enough to accommodate that extra handle height, that is), or the industrial-looking Versa case, or the flat and flimsy aluminum case. I like it for my larger tourney set. It comes in black and gray, but sometimes goes out of stock.
FOMITO AB-27B Foldable Camera Storage Bag 44x30x22cm Shockproof Case for DSLR, Gimbal, Drone Heavy-Duty Handle
https://a.co/d/03AlEUUD
The other case I use is a Koolertron (also from Amazon). It sells for $43. It’s a smaller case but comes in multiple color variations. I use mine for my smaller cash game set. My set up is 3 racks x 3 racks but there is room for a fourth row, so you could technically fit 12 racks, but I haven’t tested it yet to see if it could handle that weight. This bag with nine racks and two card setups is about 21 lbs total, and seems just about right. Again, I chose to use the included partitions to use as filler, but still plenty of room for cards, buttons, etc.
This case is even less solid/sturdy than the Fomito, so if that’s important to you, this isn’t the carrier for you. It is a little more on the slouchier side. For me, it does the job and looks clean, top handle and a shoulder strap included. I plan to get another in a different color when I put together a smaller tourney set.
Koolertron Dslr Camera Insert Bag Purse Universal Liner Lens Pouch Partition Protective Cover Waterproof Sleeve for Cannon/Nikon/Sony (Grey)
https://a.co/d/0e8YHpvL
Hope this helps! Here are some pictures of both bags (Fomito is black, Koolertron is grey):