I just bought and installed that mirror. It works great. More on reddit.com

You can get daylight-warmth LED strips which is probably what you're looking for. Typically also just have the lights recessed behind the mirror so you catch the glow instead of directly off the bulbs. You're probably thinking something like this right? More on reddit.com

I had a lighted vanity mirror/medicine cabinet, in a prior home. I thought it looked really ultra-modern and cool. But, overall, I didn't find it very practical. Obviously, the light can't be too bright, or you'd simply be blinded by trying to look at yourself in the mirror. But, without a bright enough like to shine on you, reflect off your face, and then reflect off the mirror, it doesn't really do much, and you need other lighting anyway. And, as you noted, when the light fails, you don't just pop in a new bulb, and it usually means replacing the whole thing. So, it's a trade-off--it looks great, but it's not really practical, and you'll need an additional vanity light(s) anyway. However, there is a potential alternative, and that's a lighted, pull-out, wall-mounted shaving/makeup mirror. I have one now and love it. As for lights to the sides of the vanity or above it? I always recommend above. You'll want bright light, for shaving, putting on makeup, etc. But, if that bright light is next to the mirror, at around eye level, then it can be blinding. Light above the mirror means you're not really looking directly at it. 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