How can I make over this bathroom space?

I think the shelves would look much better if they are covered in the front where the supports are visible. You mentioned not good with saws but perhaps you could use something besides wood. I would recommend luan plywood but perhaps foam board then cover with a marble looking contact paper.

wall paper it in a large print, hides any uneveness, including the pieces of wood holding up the shelves.

have glass co cut new shelves, and you will have a nice medicine cabinet.

The supports for the wood shelves could be cut back to the edges of the wall and the wood shelves replaced with glass. Of course the shelves would not be as deep--it's hard to tell what your depth is there. You could also add some wallpaper or stenciling on the wall behind the shelves. You may be able to add the same wallpaper or stencil around the medicine cabinet mirror wall.

You have several options. 1. Paint the area behind the mirror and the shelving alcove a dark color. This will hide imperfections and give it a pop. Take out the wooden shelf supports (before you paint) and replace with pretty metal brackets. You can buy decorative edging to go on the front of the shelves. This can just be glued on or attached with very small nails. Fill the gap between the shelf and the edging with White Lightning. (Make sure you smooth it out with a wet finger. You can't sand it smooth once it dries, but it dries smoothly by just wiping away any excess with a damp cloth and using your damp finger to smooth it.) Then paint your shelf with the edging and install on your new brackets.

https://www.lowes.com/pd/White-Lightning-10-oz-White-Paintable-Caulk/1000060827

Wow, you all have some great ideas. Thank you. In regards to taking out the shelf supports, my husband built them first and then drywalled around them. It won't be an easy task to take them out, but camouflage would certainly be easier.

It needs to look like all one piece. A frame around the whole thing would help perhaps made with 1 x 2"s. Then use Kathy's idea of hiding the ends of the shelf supports. Old wooden blinds slats might be perfect if you happen to have some laying around. Otherwise Look though the trim pieces at your home improvement store and try to find something the exact thickness of the overhang or a little less. Or even use strips of plywood which comes in 1/8", 1/4", 3/8" thickness. You can buy quarter sheet or sometimes even smaller pieces. Most of the time lumberyards will cut wood for you if you have exact measurements.

Another approach is to rethink what you use the shelves for. Although the green baskets are nice looking, is the space inside the recessed shelf area really being used to maximum advantage at the present time?

If you require more storage space for small toiletries, then I would suggest to install additional shelves in between the existing ones, shortening the height.

Instead of trying to disguise the fronts of the supports, use them as a sturdy backing for hooks to hang facecloths, or small attractive bags for supplies.

If you did not want any items on the shelves visible all the time, then mount a small curtain rod and 'hide' what is behind with an attractive panel of fabric.