Even cheap HDMI cables can support 4K without too much issue. Maybe not some really old ones.
To justify 4K, you really need a big TV, 75"+. At 65" maybe if you sit really close you will notice an improvement.
The new OLEDs have blacks every bit as good as your plasma, and much brighter, so better effective contrast in all lighting conditions. As you get older, a big TV can be nice on the eyes too.
Modern TVs have better processing chips so if you watch a lot of sports you may notice an improvement there. The newer TVs also support improved color depth on the HDMI, but not sure you will notice it.
Not sure the best resource. This is stuff I have picked up over the last couple years as I have bought stuff and just generally being into the tech.