I recommend "Hansong Hollywood Vanity Mirror" you can get it on Amazon for around $50. I had pretty crappy lighting and this is very bright and looks decent without being super costly. I can't vouch for longevity as I've only had it for about 3-weeks but really like it so far. More on reddit.com

I bought my vanity mirror from Lumina Pro . Haven't had any issues thus far. Super bright too. More on reddit.com

In my experience, a lighted mirror does not provide enough light to the rest of the room. After living in enough apartments that had completely inadequate lighting, if I have the option, I’ll always go for more light. It’s something I don’t think people take into consideration until they need it- a water leak at the toilet (or in this case the washer too) but you need your phone as a flashlight to try to see where it’s coming from, a pet vomits on the floor but you can’t see well enough to tell if it’s completely cleaned up, dropped an earring or a ring and, again, have to get out your phone or a flashlight to see where it rolled. More on reddit.com

Get a colour tuneable white strip. They have two sets of white LED's, one warm white and the other cool white. You can then control the colour temperature by dimming each one. Don't use RGB. They are terrible for colour fidelity because they only produce light in a few narrow bands of the spectrum. White LEDs are engineered to produce light across the whole spectrum and so they give much better colour reproduction. Look for LEDs with a high CRI rating, 90-95 if you want really good, natural colours. CRI (colour rendering index) is how leds are rated in terms of how pure the white light is. Places like art galleries will typically use 95-96 cri leds to get the most accurate and natural lighting for artwork. More on reddit.com