Hey I am relatively new at MM as well (not to Pi though). I created 2 of these so far. The first was created using the 7" Pi display. That was used mainly as a proof of concept. Once I ironed out everything I wanted, I ended up going on Kijiji and found someone selling a 22" monitor for $25. It has DVI connection but I use an HDMI to DVI adapter which works great.
As far as powering everything, you will need to power your monitor and the pi separately. You can hide everything behind the mirror with the exception of the 2 power cables (pi cable and monitor). I haven’t figured out a way around this yet.
Hope this helps.