Glass tiles, in and of themselves, have been around recently for 10 - 15 years, and historically since the early 1900's, so it is not the tiles themselves that could look dated, but the application.
In my view, you have too many things going on if you add a vertical strip of them to what you have outlined above. This will be the thing that will date your bathroom, not the materials you have chosen. Try to think of it in terms of a "vocabulary" of design, and keep things simpler. One type / size tile for the floors, one for the shower walls, and one for the shower floor, and leave it at that. Cleaner and simpler is always better, in my opinion. If you really love the glass tiles, use them on the shower walls instead of the 12 x 24s, but not both, I think. Just my opinion, but hope it helps.

Thank you for your input. Would you feel better about the glass tile strip if we used 1 X 1 square tiles, rather than the horizontal ones? What about iridescent vs. satin? We are opting for the vertical 12 X 24 so that we can use full tiles. I prefer the look of using them horizontally, but the space is too small. Any input on this?

In my opinion, it is the use of too many materials, not the size or shape of the tiles, that is the problem. I like the idea of installing the 12 x 24s vertically. You might consider putting them up in what is called "soldier course", meaning that there is no off-set of the grout lines. This is a clean, modern look, but interestingly was also done in the early 1900s. Here is a photo of a bathroom in a Frank Lloyd Wright house I worked on a couple of years ago showing a horizontal soldier course treatment of the wall tiles.

This is definitely an option. Regarding the materials, the floor tiles, shower floor tiles and shower wall tiles are all actually the same Lifestone Cross Cut Travertine, just cut into different sizes. The mosaic shower floor has color variations, but these are cut from the larger tiles.

Abbe3 Could you post a picture of your bath - I am thinking of doing something similar but not sure about the glass tiles. Thanks!