Old style looking painted furniture can look great in a contemporary bathroom. The photo above left shows a double vanity unit cupboard, the warm furniture tones contrast wonderfully against the clean wall tiles. The use of 2 different basin bowls only adds to the effect of a bathroom evolving over time. The photo above right is a single vanity unit painted Scandinavian style, with a painted marble top & light antiqued finish. Again would look good with either a sit-on bowl or undermounted sink. The size & proportions of bespoke pieces like these can be whatever you want.
You could go even more rustic & use a farm table as a vanity, which would add great character to the bathroom. While the basin / plumbing would be more visible with this option, the table shape & character are what catch your eye. Table height is the one consideration you need to make; go for a normal height table, with an undermounted sink (but waste is more visible underneath); or if you want to use bowls that sit on the worktop you would need a lower height table.