Good Day from the other side of Texas. It appears you are in a good situation for an antenna. All of your major stations come from the same direction and they are all UHF. At 60 degrees, K41EQ is Three Angles Broadcasting. If you are interested in that, it is so strong and close it will probably come in even with your antenna pointed at the major networks. KZTE appears to be off of the air. It is good you are planning on an outdoor mount though as that 1 edge designation means some of your signals are blocked by a small hill or even the curvature of the earth. The higher you can mount your antenna, the better.
I like vertically mounted 4 bay UHF antennas such as the Winegard 4400 and would certainly consider the new design of the Antennas Direct DB4e. They tend to have less wind load than yagi style antennas when only UHF is needed.
It does not matter how many TVs are on at the same time. The signal is split whether on or off. If you are planning on running cable to 5 rooms, that is a bit of an odd number. They make 2 way, 4 way and 8 way splitters and I would favor trying a non-amplified system first. However, if you can not live with just 4 rooms connected, you probably will need to look into amplification. Hopefully another knowledgeable member will advise on that as I have never been very fond of amplification. I have seen it cause more problems than if solved.
So, at least this will give you some material to research. Your goals seem quite attainable.