Here is your dilemma. if you take down those fixtures there will be two holes in the mirror, that being said, they will be up high and most likely off center. So, to get new lighting that is not stuck in the corners, and covers the holes behind it, might be next to impossible unless you run a thick bar that covers the space. But some times back in the day they only drug wire over and did not put in actual junction boxes, so the bringing it to code might be another issue. 1. take one of the lights down and see what is going on 2. probably have to replace the mirror and move the electrical location.

if everyone that uses the mirror is approximately the same height, that would make choosing mirrors that showcase your new tile easier. If you have two mirrors the size shown, you could reuse them, hanging them horizontally, with or without frames. If you want the overhead boxes and light gone but do not have enough tile for that part of the wall, you might consider covering the area with paneling into which you can recess new LED light fixtures or against which you can attach your new light fixture -- or both. I'd want more recessed lights than this one but also like the idea of a second light fixture on a separate switch outside the box in which the recessed lights are installed that could light the entire room. https://www.wayfair.com/Winston-Porter--Whelan-5Light-Dimmable-Vanity-Light-X111249349-L6116-K~W000138238.html?refid=GX433803226217-W000138238_1811975260&device=c&ptid=903084850761&network=g&targetid=pla-903084850761&channel=GooglePLA&ireid=64738416&fdid=1817&PiID%5B%5D=1811975260&gclid=EAIaIQobChMI3NDB0few7wIV__DjBx0YXgrfEAQYBCABEgKfv_D_BwE

If budget is a big concern I would look at painting the cabinet and replacing just the doors and drawer fronts and keeping the boxes. Wouldn't bother with the mirror. Get new lighting and new faucets. I didn't notice that the vanity in my master had an 6" space between the vanity and wall when I bought my home - I mean, I knew it was there, but didn't think about it, until I moved in. What a PITA. Awkward to clean and a magnet for makeup and hairbrush or toothpaste . . . everything seemed to drop into that little space and then my dog discovered the space - great place to shove her ball and then bark at it until I would retrieve the ball. It was the first thing I renovated in my home. Other thoughts really depend on your plumbing and needs. My home was built in the 1960s and was a luxury 2000 sf, 2 bedroom, 2 bath home in it's day, but styles have changed since then. I love my hall bath. It has an 8' vanity with just a single sink in the center. I love the luxurious look of this massive expanse of counter space and it provides ample storage. My master vanity is not as large and again, just has one sink. It was a 48" vanity with a 24 center and 2 12" banks of drawers with the 6" space between the wall and the vanity. The plumbing on that wall is really hard to access or change, so I kept the sink where it was and just changed the vanity to a 15" bank, 24" center and a 12" bank and added a filler piece against the wall. Couldn't do 18" drawers or the drawers wouldn't open due to hitting the door trim. I had to replace both mirrors and they were glued to the walls. We were able to remove the mirror in the front bathroom and fix the drywall, but the master wasn't budging. We ended up cutting the drywall to remove the mirror and just replaced the whole section of drywall over the vanity. Having single sinks instead of giving up drawer and counter space is not a bad tradeoff. You spend only a few minutes at the sink brushing your teeth and washing your face and much more time standing in front of the mirror doing hair and makeup.

Like Jan and Beth said, you putting the cart before the horse. New home - live there for 6 months to a year before doing any major renovations. During that time prioritize your needs, wants and like to have renovations and figure out the budget for renovations. Every renovation you commit to will take twice as long as you think it will and cost twice as much as you think it will. Budget should be dependent at least in part to the amount of time you believe you will live in the home. You should also be exploring your style and color selections. Once you have a solid budget you will know what things must stay and what you can afford to change and what elements you don't want to change. Once you know what has to stay you can design around those elements. Do they work with your preferred style and colors? What compromises will you need to make to create a cohesive home? I am not a contractor, but if you are planning on expanding the shower I am pretty sure the old shower has to be re-tiled. The whole shower has to be water sealed and that seal is under the tile. I don't think you can save the tile in the niche.