What a cute bathroom! If it were mine and if the tile were in good shape, I'd leave that in, although I don't know if tile can be made glossy.

Other suggestions: Since you already have storage and a medicine cabinet, you might install a pedestal sink for a more "complete" look. Leave the ceramic cup/soap holders in place. For window treatments in our bathrooms I put up simple white café style curtains (from Country Curtains) on a tension rod so that they just cover the window itself. Then weather permitting the window is left up a bit, so there's always a nice breeze behind the wafting fabric.

I also prefer a shower curtain to glass doors, but what with the children, you may want the doors there.

Nice project with many possibilities!

Love it! Don’t know about making tile glossy. I doubt that could be done. Just do get rid of the glass slider on the tub. Easy to do. Put in a shower curtain and you’ll be golden.

You could try a topical water based sealer in a gloss finish. May or may not work. It's a small room so removing it won't be a huge chore.

First, congrats on your new place. I wouldn’t touch the tile, they look like they are in good shape. The way old tiles were made is what makes them so durable. I have vintage tile in my guest bathroom too, and as My3dogs mentioned, make sure you’re not missing tile behind the vanity (ours is missing). If not, pedestal would be great!

Turn the toilet.

Vintage bath; I suspect a wall hung lavatory was original so, hopefully, there is tile under the vanity.