Don't know how many tubes you want to keep track of. Personally I probably have around 300 tubes. As the excellent work of the people on this forum progresses I am buying new tubes that show great promise in sound reproduction.
Therefore I end up with a large amount of tubes that I don't listen to any more. Many of these I bought without boxes. I found an inexpensive way of storing them in plastic boxes made for nuts, screws or small parts etc.. Some of these boxes have movable dividers. I took along a couple of tubes to the hardware store and picked a box that accommodated the sizes I needed to store.
For around $6-7 I got a box with 48 compartments. Then I sorted the tubes and put them into the compartments with a sticker on the lid corresponding to the contents underneath the sticker. Here I write brand, dates etc. One box can store around 120 tubes without boxes, and I can vary the sizes of the compartments by moving the dividers if I have 4 or 10 of the same type of tube. (If a compartment is not full, I stick in pieces of foam "peanuts" to keep the tubes in place.)
It may be hard to grab a tube to get out of the box. On the suggestion of Mikeleap (?) I bought rubber fingers in an office supply store (size XL is the right size) that makes it easy to grip the tubes.
The new tubes I am buying now usually come with boxes. I just store them in a shoe box with rubber bands keeping the same type together. Ultimately, I end up with a few favorite tubes that get their own special box.
If you have much larger quantities in tube boxes I could imagine a shelving system of some kind.
I have to admit that I keep most of the currently used tubes committed to memory. Stick the hand into the shoe box, under the the pieces of bubble wrap, left corner top, in unmarked boxes - yep; there are the Tektronix 6AU6 that I want to try. I'm afraid that if I get too organized I would not be able to find them.....LOL
Don't know if this is helpful....Good luck!