My first major objective was taking out Monaco, to test out combat, capturing cities. Plus, they were directly to the south of my capital, so it seemed wise to absorb them. I saved before going to war, and it took a couple of times to get it right (as in having a decently big enough force), but it taught me about how big a force I need.
The first city state I really made an effort to befriend was, ironically considering my screen name, Geneva. More because I like the cultural benefits *a lot* as the social policies do seem to be a nice boost.
Meanwhile I decided to needed to try out a full scale war, and to be perfectly honest I love going more a militaristic route in the Civ series anyways! So I looked to where I wanted to expand. I decided conquering Japan would allow for some open territory to settle, so I elected to conquer them first. Figuring I could conquer out to the west for a while, before turning to the more clustered east.
I quickly took Osaka, overwhelming them with 3-4 legions and a couple archers. I annexed it, and left some pikes to defend. I advanced on Kyoto, and my forces (although drawing quite a bit of blood from the Japanese military) was rebuffed a couple of times. Thankfully, it was a ratio that I could afford in the long run. The Japanese offered peace, giving me Tokyo and resources, and I agreed and rebuilt my forces. When the peace treaty was over, I swooped on Kyoto and captured it. Japan was my first full conquest in Civ 5. Tis a shame, as I was really hoping it'd be Gandhi after all those times he nuked me in previous Civs!
In these conquests I gained my first Great Person, Robert E. Lee. This is pretty cool as I share the same first two names, and I am an American Civil War buff.
Geneva wanted me to capture Genoa, which thankfully, was just to the west of my newly acquired territory. Conquering it, I was *strongly* liked by Geneva. Though the city states are apparently banding together due to my conquests.
I've recently decided to turn on the Aztecs, having upgraded much of my offensive force to rifleman. They're doing quite well, and I got to see what embarking and all was like. Very simply, but I was nervous that embarked pikes might pose a threat to my embarked troops.
Though I do think I have a clear military lead if the image below is any fair indicator.