Put a heavy cloth [folded towel, etc…] over the front portion of the shade facing the TV. That will block the light going toward the screen but still allow light to the sides and back for work/reading. Adjust coverage to eliminate/reduce reflection to a suitable level. Martha Stewart will be along shortly and have a more elegant solution but this works well.
I’d look for more of a “reading lamp” than a general “desk lamp”. Reading lamps tend to be more directional, like this, so you can focus the light on whatever you’re doing with very little, what would you call it, “oversplash”? They also make torchiere lamps with a reading lamp attached, like this one, so you can have both in one unit, if you need a general lamp as well.
Polarizing your light only reduces reflections at angles where the incident & reflected light are fairly oblique to the reflecting surface (making about a 34[sup]o[/sup] angle with the surface for a typical glass-air interface.) For the geometry the OP is talking about, the light is hitting the TV glass at pretty much right angles, so polarization won’t help.
Seems to me most of them could work, offering at least some improvement over a standard table lamp. However, someone working at the table would want to angle the shade away from his eyes, which would send more light towards the TV. You might need a homemade shade extension to prevent glare in the TV. One could be cut from black construction paper or poster board and taped to the lamp’s shade.
I mention this only because it includes a feature not mentioned at the site or in the accompanying literature.
Once you’ve settled on the angles you want in your lamp, you’re supposed to screw the “joints” tightly to lock it in. But - and here’s the Skull and Bones secret never before revealed - there are little threaded set screws in the horizontal bars that you can tighten instead, using the tiny Allen Wrench supplied with the unit.
I like this thing. The halogen bulb can run hot, but the lamp has a built-in Dimmer Switch that lets you run from full off to full power.