A lot of the info below is my own personal taste- feel free to email me with your comments.
Things to ask yourself...
1) Will anyone linger in front of the monitor?
If someone is just going to walk past, without lingering, then just leave the monitor turned off. Don't worry about making it blue or green. If there is a lot of occlusion, you will probably want to make the monitor keyable. See below for more.
2) Are there reflections in the monitor that you'd like to keep?
If so, you should either leave the monitor turned off, or have video playback run a solid signal to the monitor. If no one is crossing the monitor, you can use a grey screen that changes every few seconds. This will solve your interactive light problem too. If your TV is in an environment with recognizable reflections, consider photographing your scene "from the TV's point of view" for the maximum control of reflections. Still photographs will also work. If you're shooting reverses anyway, just supply a few of these to the VFX company and they well thank you for it. Simple stuff like highlights and random reflections are easy to add and contribute to the realism of your shot.
3) Will the monitor be casting light on your actor?
If so, go ahead and 'fake it' with some interactive light. But go easy. It's also fine to have video playback play some similar material through the monitor, especially if your live action characters are not crossing the picture.
4) Will you be intercutting your composited footage with practical footage of the same TV?
If so, make sure that you send a scan of what you're matching to to your VFX company.
5) Where will the material that's going INTO the TV come from?
If you can, SHOOT THIS ON FILM. If you can't get that together for some reason, consider shooting 24P HD or HD PAL. If you shoot it on NTSC DV or some other format, remember that the quality of the comp is only as good as the source footage. Also remember that NTSC runs at 30fps, and film runs at 24fps. So if your characters on TV are talking, you will have some issues. They aren't insurmountable, but the conversion from 30 to 24 does have visible artifacts. If you shoot PAL, it's best to repitch the audio to match the picture.
6) Compose for your destination frame
If you're comping into a 16x9 TV, take this into account when composing the footage that will fill the TV.
7) Is the camera moving, and will the edges of the monitor break frame?
If the corners of the TV break frame, you may want to add a tracking marker on the monitor surface which remains in frame. If your monitor does not leave exposed frame (not just your projection frame), don't put any tape, tracking markers, or anything else on the screen. The corners of the monitor make excellent tracking points. If the corners are especially rounded, then it's okay to put four small ROUND dots in each corner, positioned about 1/4" from the corners. If you are shooting 1.85 or super 35, remember that lots of extra information is saved on the negative outside the projected area. So go easy on the trackers! If in doubt, just put four small trackers in the corners of the picture, and maybe one in the middle.
Tracking dots on a curved screen No trackers necessary
7) Does your TV have a logo or brand name that your movie studio will object to?
If it's a Sony picture, they won't want a Samsung logo in their movie. And nobody but Sony wants to see a Sony logo. So now is the time to cover it up! Take the time to get your set decorator to do it nicely. You'll thank yourself later.
How to make a monitor keyable:
Remember that if no one spends time in front of the monitor, the best thing to do is leave it turned off. If your actor spends more than a few seconds in front of the monitor, then try one of the following steps. My favorite way is to get your 24 frame playback person to broadcast a frame of blue through the TV. This looks most natural, and is easy to set up, and it lights itself. It you can't get that together, then get DIGITAL GREEN tape and plaster it as smoothly as possible over the screen. You can also paint the screen. The exact color is not terribly important- you can buy the cheaper "digital green" paint from Roscoe. I don't recommend skinning the screen with fabric. It tends to obscure the edges of the bezel and also has a fuzzy edge.
What NOT to do:
1) DO NOT RUN STATIC THROUGH THE MONITOR
I don't know why people do this, but it makes the tracking difficult, it prevents the artist from extracting any reflections, and it casts a really ugly noise pattern on anything close to the TV.
2) TRY TO FOCUS THE CAMERA
Yeah, it sounds stupid, but people forget to do this all the time. Nothing kills a monitor comp like a sharp picture in a soft frame!
3) KEEP IT STEADY
If the shot's a lockoff, ask the camera operator not to bounce on the dolly while he's shooting the scene.
4) KEEP IT STEADY (2)
When shooting the FILL material for the monitor, use a tripod! Unless you're trying to make the next "Blair Witch", nothing looks cheesier than bouncy footage in a TV. Of course, you can stabilize footage, but you have to blow it up, which will cause problems with composition, especially if you shot on NTSC.
Following these steps can make the difference between a $1000 comp and a $5000 comp. And as we know, comps tend to multiply. Every dollar counts!