I really like the design for a flat screen cabinet. You needn't be worried about a 26" widescreen being mounted to 3/4" MDF like this. It will hang fine and be plenty sturdy, so long as you aren't stingy with the fasteners, and use a couple on every panel it overlaps. There is also nothing wrong with the distance. Regular game setups put the screen literally right in front of the panel. My 27" RGB CRT is situated like this, and It feels fine to me. The fact that you are using a 26" widescreen, which is smaller than a 4:3 monitor of the same size, and it has some distance to it, all works in your favor. As for height, I think lower than the eye level of the shortest individual likely to use it, will be much better than higher. It's much more comfortable to hang your head than hold it tilted back. It will also make it less "tippy".
But I do agree with the comments about base size. For something this tall, the base may be a little small without a pedestal of some nature. As someone already mentioned, a lot of weight in the base will work as well. If you want to get fancy, you can make feet extend off the side edges of all of the panels, toward the bottom, and slot them so they interlock.