i had the same issue. I ended up with a great vanity from Ikea that's modern/ midcentury style. It was easily half the price of any other vanity i looked at that i sorta-liked online and it includes the integrated sinktop + single hole faucet.
You could even get custom doors from semihandmade to match that rustic wood look you're after.

Yup, IKEA... get drawer fronts made in the style you want if nothing they have suits you.

Have you considered having a vanity cabinet made by a cabinet maker and having the countertop fabricated? That would likely give you the most customized options.

I ended up finding a vanity that fit an unusually sized space for double sink from Home Depot. Marble top with undermount sinks and legs, but simple shaker styling rather than fussy. I was surprised at their selection online. And they had an extra small charge to deliver to the desired room (which was great since my bathroom was on the second floor). It ended up being an almost perfect match (except square vs round sinks) to a Restoration Hardware Hutton vanity I put in a nearby bathroom and was about half the cost.

I think a lot of free standing vanities are cheap. Have a cabinet put in that matches your kitchen cabinets. On a new build they can order it all together and save you money. You may have leftover countertop material to use for the top at no extra charge, or you can look for a remnant piece. That will also give you the best storage.

nice find, @mdln

It's mid-century modern style but I like the Joel vanity from Wayfair... If you like that look but want to spend more there's the Berkeley from Room and Board, Mid Century from West Elm or Franca from PB.

Check out fairmont vanities.
Fairmont Designs 1505-WV30 m4 30" Wall Mount Vanity in Natural Walnut

In addition to Fairmont Designs, you can also try Empire Industries.

You guys are awesome!! This is my first post and SUCH helpful responses, thanks so much!! Will look into all of these options. Much appreciated!! :)