First things first, I would try putting a larger mirror on the wall above your desk, instead of just using a smaller tabletop mirror. This will help make it feel like an established vanity.
As far as lighting goes, I suggest daylight bulbs. They cost about the same as ordinary lightbulbs and have the same color temperature as sunlight, as opposed to the yellowy cast of tungsten. If you just pop one of those into a lamp, you’ll know the lighting you’re working with will be the same as if you were outside in the sun! Super helpful when doing makeup.
Those two easy changes should make a big difference for you! No Hollywood set up required!