Do you have a HOBO (home owners bargain outlet) near you? You can find some super deals at these stores.

With a limited budget, I would remove the oak/shelf cabinet .. replace with a piece of art (maybe you already own something you could hang there)

Use the art as a color guide for paint on the walls.

Replace the cabinet handles.

You must have a new vanity top. Here's a nicely designed inexpensive one from Lowe's. Get a cute chrome or brushed silvery color faucet and knobs. Paint the vanity Sherwin Williams "caviar" satin finish (soft black) and the walls Sherwin Williams sea salt (pale greenish-gray). Use simple wood molding painted the same color as the vanity to frame the mirror or buy an inexpensive mirror framed in silver metal (think Lowes has that too). You don't show the vanity light but if it isn't silvery-colored, get a new one that is --preferably with square frosted globes. Here's a great one. Look for a small seagrass rug for texture. And definitely take down the wall cabinet. The space will seem MUCH larger. Hang a piece of art there, in soft colors with a lot of white in it. sized a bit smaller than the mirror, framed in a light wood. Good luck!

Oh yes you can replace that vanity top! You must! Plus. Buy some paint

Sorry, wasn't finished.
Get a new faucet, too
See initial post..... Then, place some molding around the mirror, remove all the plastic bottles of stuff and store them aay. Install some nice towels holders with folded towels, and them some art,
Have fun!