Matrix switch will definitely be in your future. Many good ones (read: not cheap) will handle IR routing/repeating as part of their solution.
The matrix switches climb in price rapidly as you bump above 4 sources, and certainly above 8 displays. If you can subdivide into two "groups" of displays (therefore using two small matrix devices), you can save a bundle at the cost of some limitations and/or complexity.
Do figure out what you want to accomplish, though - is this to "share stored content (DVR)", "keep displays in sync", "move from room to room", or "save money on set-top box rental". The last one, in terms of a large-ish matrix, is probably not a good idea on its own. Even $10/box rental could take years to payback for a large matrix.
On your cable box count - a good rule is to start with one box per family member / viewer.
But let's not get too far ahead - concentrate on getting enough wiring to enough places first, and the equipment choices. Matrix switch solutions will need 1-2 cat5e/cat6 lines per display. The best technology, HDBaseT, only needs one, but I would wire for 2-cable solutions. Actually, I'd still recommend at least a minimum of 3 cat5e's per display location.