I understand better now, but not completely. Yes, 2 (or 3) gang in the built-in cabinet. 1-2 keystone plates, and 1 pass-through/scoop plate. Pass-through plate for HDMI to the TV, and possibly your 'balun' category cables.
Why 2 HDMI cables to the TV?
What is the 'balun' for? If you're using an HDMI extender of some sort (HDBaseT extender may be better), you would want to avoid the extra connections of keystones, and use the pass-through plate. Extra connections may degrade the signal.
Behind the TV you'd use a scoop plate, for the HDMI cable(s). And, don't forget TV power. Combined power outlet and LV TV box is a good solution. 3 Gang TV box would give you a keystone plate, pass-though plate, and TV power.
Don't forget LAN connection to the TV, for internet (firmware, internet sources, IP control). I suggest you use a small 8 port gigabit ethernet switch in the built-in cabinet to supply the TV, cable/sat box, AVR, BDP, and any other devices that could use an internet connection. Extra category cable would give you an Audio Return Channel from the TV to the AVR; not sure how that's helpful, but I've read of others doing it. And, another category cable for IR to the TV, from the built-in cabinet. I would add 2-4 more category cables, run from the built-in to the TV, for possibly replacing your 1-2 HDMI cables in the future. Really, can't have too many category cables, and if DIY, and you're buying the box of cable, there is no added cost. I'd just use cat6 for everything. Just leave the unused category cables unterminated behind the plates.
I don't understand what you mean by 'structured media center'. Is this a low voltage enclosure, e.g. the Leviton SMC? If yes, then no, you wouldn't use any wall plate for that. The enclosure is basically a giant wall plate. Cables run into the side of the enclosure, and are connected to your equipment in the enclosure (modem, router, switch). A LV enclosure usually has a power outlet inside of it.
This video from Leviton shows how to install a LV enclosure (the Leviton Structured Media Center). http://www.youtube.com/watch?v=jti8_10aLk4
You may want to consider some wireless access points, depending on the size of your house.