During back to school sales, lots of items are available to help organize small items. I like the small pencil cases that are about 1" deep, 3" wide, and 8" long and the interior is a tray that slides out. They have a snapper closure and are semi- rigid plastic. I have paid .50 cents for them. The 45mm Olfa fits perfectly in the case. I've given lots of these away.

I put it in one of those clear zippered plastic bags that pillowcases now come in. I usually put the rotary cutter, blades in their plastic case (when you buy 5 at a time) and my klutz glove all together. When I'm at home, it hangs on my bulletin board above my sewing machine. I have a cat that jumps up on the sewing table and I have to have the cutter up and away from her paws.

If you drink crystal light, the containers are the perfect size for carrying rotary cutters.

I bought a cheap pot holder from the dollar store (rectangle) I folded it in half and sitched up the side and bottom. Now I put my cutter in this before putting into a zipper container, or my stackable container.

I would be reluctant to just toss my rotary cutter into a bag, I would probably use an eye glass case, a hard one if you have it, but another type if you don't; just to be on the safe side. I have seen in various magazines where someone sewed over a pot holder on 2 sides, which would be safe as well.

I always lock my cutter now, even at home. When going to a class or sewing meet, I take my tray that is always next to my sewing machine. It is a Tupperware Modular Mate rectangle one: a box about 7" X 10" by 2" high. With that cover on, everything is quite tight in there. I have a bobbin donut with a pin cushion in its center, and the other stuff I need all around. My cutter fits as well as 2 pair of scissors. Most used presser feet and a few skewers are always handy.

I bought a plastic storage box at Joann's that has little sliding latches on it. I keep all my rotary cutters in it, then padlocked. I even do this at home. I have small grandchildren and little ones can get very curious. (even though they are not supposed to be in MiMi's sewing room). I would feel TERRIBLE if one of them got a rotary cutter and hurt themselves. The key to the padlock is kept up & out of site. As with guns, knives, etc. we are educating them as we go. But, until they are all old enough to understand the consequences, they will be kept under lock & key.
This is just my idea and the way I do it.

I'm a total newb, but would a fishing tackle box be a good holder with compartments for needles and small tools of various sizes?

I have everything that cuts (rotary cutter, seam ripper, snips etc) in a small zippered case. Most rotary cutters have safety locks. I haven't had any trouble in route with anything being cut.

I use an eyeglass case that snaps shut and a cloth one with a snap.