Military
Say hello to your beat stick. Can’t avoid this bad boy as this is a war game, and if you want to be successful, you need a strong Military officer. He has a few uses so we go through them in order of importance from least to best. 1st as mayor: Your Military officer reduces training time of all units and defenses. If you want quick troops appoint him as mayor, train them (as soon as training started) then shift back to Politic officer as you only needed him in the position to initialize the training to get the reduction bonus. 2) he is your attacking officer. His military score raises your Attack (10 points per 1 military point) and your Attack score affects your bonus damage percentage. Consider the quickest way to raise your rank is off of NPC Cities and the backs of other players, having one very strong Military officer is key. I would not suggest more than one per city, as you need room for a lot of politics officers.
Knowledge
This guy is similar to your Military Officer in multiple respects. You want to find a 4 Star level and level him up as soon as possible. His score is extremely important for saving you huge amounts of time in your overall improvement. The most important aspect of the Knowledge officer, is as a part-time mayor. Never start researching a new technology without first appointing this guy as your mayor. But like Military officer, once you’ve started the tech, immediately go back to your Politics officer as mayor. Like your Military office, your Knowledge officer increases your Defense stat by 10 points per ever 1 point of knowledge. However, a really good Knowledge officer has an attacking use. When hitting NPC cities for officer experience and raising your rep, you always want to plunder first, and then seize. The plunder should be conducted by your Military officer as you can clean out the troops with less losses. However, your military officer has no real bearing on a seize. You are going to loose troops on an NPC seize you can not out range their howitzers and Anti-tank guns, so in order to counter these losses, using a solid Knowledge officer is the key, as the stronger his knowledge stat gets, the fewer losses you will take.