Hi, cflaherty. Seems you've landed your architectural dilemma on 'The Laundry Room Forum'! ;~) While we have some very talented folk here, don't know if they know much about remodels?

When you say "shower door," it can mean any of dozens of product offerings. Chances are this is a simple service call adjusting the hinge. Do you have some pictures of your enclosure?

On first thought: as little grain as possible, or loud contrast I suppose, cause your doors have much grain I am thinking-- in them. And choose a tile that compliments them, and save repainting. You can sand and revarnish them, also? But anyways, I found this brand. I would love 3 of them, depends on the colors and the door stain/other decor, in your home: Adura Calypso Mist, Seasiders, or Graphite Charcoal Flax, last one, because it catches the cool and the warm equally in a home I expect..Corsica could be nice if your home is generally light and again, depends on your wood stains and painted walls and decor colors...Which one works, if any of them? https://tmcarpetandfloors.com/vinyl/mannington-luxury-vinyl/ Canadian Maple is a great color, but the contrast may just be too busy with your doors, or it may be just the right tones? The other 3 or 4 may be better tho?

They are full glass. If someone wants to break in, they can always break the glass. The double door with inswing and center hinge is usually not terribly secure as it can be kicked in but you can use a deadbolt to help with security. Sliders can sometimes be taken off the track. We have a drop-down bar (easy to buy and install) that goes across the center of a slider to prevent the door being opened/taken off the track. So the glass would have to be broken to get in, as near as I can tell. It was already on the door when we moved in-- I would probably not have installed it. If both doors on the inswing were operable, that would be my preference because I could open up a wide area for passage back and forth to the deck and have nice breezes (hopefully) coming through. But since one door is fixed, I would get the slider because it won't take any swing-space into the room. If you don't want someone to break in as easily, use a solid door with a deadbolt into the wall side. Just my opinion :)