I’ve been working on my MM for a few months now and have had a lot of time to think over my decisions along the way and what I’ve determined is that choosing the monitor is perhaps the most important step so this is a great question. Based on what you want out of your mirror and how much you are willing to spend, the monitor you choose can determine a lot about how you approach it and what options you have.
First and foremost, I think most people would agree that a computer monitor is better than a TV for this unless you want to go really big for the display. Monitors display text much better than TV screens and since a magic mirror is predominantly text on display, then it will always look better on a computer monitor.
So the first thing I think you should decide is whether the display will fill the entire space behind the mirror or just a portion. If you decide to have it fill the space, the mirror and frame will absolutely need to be custom sized to fit around the dimensions of the monitor so they’re all about the same dimensions. If you want it to partially fill the screen then you can get any frame/mirror that work together and place the monitor wherever you want. This second option will generally be less expensive, especially if you don’t have the means to create your own frame and want to pick up one with a deep enough rabbet to fit all of the components.
I personally went all out on mine when it came to the frame and mirror glass (custom frame from a local shop and cut two-way smart mirror from twowaymirrors.com - they cut it to the exact size I wanted, I highly recommend them) so I wanted to spend as little as possible on the monitor. I managed to find a decent 1920x1080, 21" TN monitor for $60 new with built in speakers - the speakers are only 2.5w so nothing special but they’re very low profile, easy to incorporate into the mirror and already have the connection to the monitors power board which means I wouldn’t need an external power source for them. It’s probably the easiest way to get sound on your mirror aside from plugging in an external speaker but then it’s not as clean as you’ll have a wire running from your mirror to the speaker. If you don’t need sound then you can probably get a monitor like that for even less than that but keep in mind, in this price range, any monitor you get will likely have a DVI input and not HDMI so you’ll need to buy an additional DVI-to-HDMI cable or adapter. Still, the same monitor I got with HDMI was $40 more so grabbing a $10 cable was well worth it, plus I could buy whatever length of cable I wanted (rather than being stuck using the included one which could be as long as 6-feet and take up more room inside the mirror).
As @BKeyport mentioned, the ports should face towards the bottom of the screen not out the back as this would require you do have a much thicker frame to contain the cables. One other thing I did was to find the lowest profile power strip with USB that I could so I can plug everything into that and have a single cable running from the mirror to the wall. This is the power strip I ended up using. It’s 1.625" wide so it’ll fit into most builds and gives you two grounded power outlets and two USB ports for whatever you decide to include. As of now, I’m only using one of each for the monitor and RPi but if I add LED’s at any point, I’ll have the option to use either of the other two for that and still have an additional option to expand features in the future.
Sorry, I know I sort of went off the handle with my response but hopefully you found some more useful info in there! In summary, don’t worry about the specs of the monitor as much as you would if you were using it for a computer. Any monitor will display text better than a TV and other features such as size, depth, etc. are more important for the MM build, in my opinion. The one exception may be brightness/contrast if your two-way mirror is on the darker side and want the display to be vivid.