What an efficient little bathroom. Love it. If the shower is not leaking or in need of repair, I would not gut it. If you can regrout it to make it look nicer, that's great. The tile is very neutral and will go nicely with your wallpaper.

I would use a small white hex floor tile in here. It will compliment the shower and wallpaper. It will continue to go with most other future wallpaper choices you use in here, and will be neutral enough to look good with your current and future guest bed flooring choices.

Thanks! BTW, the photo makes the carpet look much darker than it is. It’s a light more beige/mushroom color.

The shower may or may not get a full gut.

If the shower is in good condition, I'd leave it be -- give it a professional clean, then decide about the re-grouting. Showers cost more than you'd expect, and yours looks good "as is".

The guest bedroom, garage door entry( to right in photo) with wood flooring and bath all come together.

The floorings look fine. Yeah, if you were starting from scratch, I'd say skip the carpet /go with all wood, but since it already exists, I wouldn't do a thing. No one's going to notice that three floorings exist ('cept you).

I have been thinking of a white/blue tile

What's your motivation in doing a new floor?

This isn't a popular opinion, but I prefer sheet linoleum over tile. Tile is cold and hard. Linoleum, which lacks grout, is easier to keep clean and is more waterproof.

I like the idea of blue and white tile.

Mrs. Pete, I am with you on tile in most situations because it hurts my feet! However, in this case the linoleum is coming up around the edges and is about 25 years old. Because it is a guest bath, I like the idea of a pretty tile. I am also really happy to hear 2 votes for keeping the shower basically as is.
Here is a tile I’m looking at, or at least, hopefully something similar not in marble:

https://www.bedbathandbeyond.com/Home-Garden/1-x-2-Basketweave-Marble-Mosaic-Tiles/39308877/product.html?recset=f8104d52-56b5-45c9-980e-3b7416ebedf7&refccid=BLNMTOVOGHQ33HSBLROLEF5Q3I&lyceumGuid=d6b50d65-e415-4357-a029-52bf7895ebfd&recalg=10000&recidx=5&osp=true&option=80143484

Anne Disney, that's a really nice tile choice, and that bit of blue isn't going to tie you into a color that'll be difficult later. I'd still consider a new linoleum for the reasons I mentioned above.

I’ve read some bad reviews from Bed Bath and Beyond.com. Check Consumer Reviews. I f you love that tile, I would try and find it possibly at a tile store near you.

I'm not a fan of the tile you posted, but it is not my house. The medallion tiles like that seem dated to me. Also, it locks you into a certain color combination and has additional grout lines. Ditch the Laura Ashley look and step out of your comfort zone a bit. What about a porcelain tile that looks like granite or marble and has some blue in it like the example below?

I also am not a fan of the light purple cabinets and trim. Paint the cabinets a dark blue, since you like blue.