$300 is a difficult hill to climb with many options for vanities including sink with regards to variety. We buy an enormous amount of vanities from various suppliers. I typically tell my clients to anticipate $400-$500 at a bare minimum to have any selection on a smaller vanity (and that typically doesn't include counter/sink). I just bought two more 36" vanities today (and spent a lot of time trying to find the best value/design, and both were right at $625 including sink and counter). One thing you could try to consider would be finding a 24" modern piece of furniture on craigslist, or whatever commerce place is available to you, and then finding a vessel sink that could work....more work for sure than buying off the shelf, but can also give you some interesting design options.

Your budget is the issue. Nothing available at that price range but cheepchinesecrapola. Any decent quality American made product will be $300+ to +++ per foot and not include any counter or plumbing.

Wait until you have $1000.

I've never done it but people have gel stained their cabinets. I think if the cabinet is in good shape, you could do something like that and get a new faucet, and counter top.