Top 5 best civs and why.

It all depends of preference, but these are my go to Civs:

Japan: While Zeros are relatively useless in actually determining the result of a game due to the era they come into play, Japan makes up for it with Samurai, which arrive at a good time in the game, and can really make a difference. Bushido is immensely powerful, and I find that low-health units have so much power that I rarely use instaheal.

The Huns: Battering rams and horse archers are so ridiculously powerful units that knocking down your first civ with the Huns is too easy. Razing cities faster isn't that impressive to me personally, but starting with a free tech is nothing to laugh at. Plus the free hammers from pastures are very good.

China: Chukonus can take down cities very fast, and with the improvements made to citadels in G&K, having a lot of great generals is not so bad. Plus the great general combat boost is like virtually having a huge mobile combat bonus.

Spain: Tercios absolutely destroy everything. End of story.

Greece: With two outstanding unique units that come in at around the same era, Greece is great for early rushes. I would argue that hopilites and companion calvary are useful into the dark ages. Plus I guess you can get militaristic city states pretty easily.

I'm sure I'm going to repeat others thoughts, but here's my 2 cents:

1) The Inca - All time favorite. All around great civ, capable of easily going after any victory condition. 0 and 1/2 price terrain improvements, no movement penalty on hills and the powerful terrace farms. Upgraded Slingers just sweeten the deal.

2) England - Mid to late game domination with LB's and SotL's, and a free extra spy. Really underrated on land based maps I think, but still just as easy to reign supreme with upgraded LB's, at least until more advanced units become the norm.

3) China - Chu Ko Nu's and Paper Makers. Early game domination is the way to go with them and spamming citadels with GG's.

4) America - B17's and Minutemen rule the mid to late game. Upgrading both makes for formidable units. Manifest Destiny is great for early game expansion, and scouts starting with +1 sight makes grabbing goody huts almost a no brainer.

5) Russia - I really like their resource UA. Couple that with the Autocracy tree, and you get +200% uranium for late game nuke fests. The Krepost is a great upgrade for a required building. The Cossack is nice, but situational I feel depending on the map type.

For warmongering?
1. China. Their Chu-Ko-Nus and extra 15% combat bonus from great generals is a no brainer. Paper makers increase science without taking away gold, so you can afford a bigger army.
2. Mongolia. Keshik, Khan, nuff said.
3. Greece. Good early UU's and can transition into diplo later.
4. Germany can get good landschnedt timings, and -25% land unit maintinence is great as well.
5. America is a good late-game warmongering civ with the minutemen and b17's.

It's interesting to me how much more people are noticing Camel Archers in GnK. They aren't that much different from their incarnation in vanilla; they were pretty much Keshiks-also even back then.

Bushido is an interesting ability. The increase in HP affects it in ways that you don't generally expect.

In vanilla, the low HP threshold and the position and upgrade strategy around Samurai meant that Blitz is the promo to get. Your unit hits twice and unlike a normal unit, his second hit is just as hard as his first. It was necessary to maximize hitting power this way to leverage Bushido because units didn't last as long; so you hit twice, then retreat the unit to heal.

Interestingly, in GnK, the modified health/damage mechanics means that Japan would really rather get March and then utilize Bushido not to pack a mean one-two punch, but to cut out healing in a relentless assault.

A normal Civ would field units, and then draw them back for healing as they get damaged. Japan doesn't need to do that. Until a unit is actually dead, their units hit just as hard as full health, on offense and on defense. This means that unless a unit is going to be counter-attacked on the next turn, it is safe and profitable to attack with it until it is nearly dead. Conversely, a Bushido unit on defense can take on and defeat multiple enemy units and give back pretty hard, meaning that a melee Bushido unit can decimate enemy units on the defensive while it's being whittled down. This means significantly less powerful attacks from those enemy units on the next turn.

Bushido Archers and Cannon are good in a different fashion. What Bushido means for them is that they don't need to heal and retreat in order to maintain firepower. A normal Cannon can position itself and set-up, but City battery can significantly reduce its firepower before it actually attacks on the next turn. This can fatally blunt a city assault if you only have one Cannon. A Bushido Cannon isn't affected the same way; it retains its full firepower even when it's at half health.

This means that you can allow ranged units to remain on the field for more turns and they hit harder while they're there.

Samurai Open Terrain free promotion has two chief advantages: Siege and Medic 2. Siege Musketmen are self-explanatory, but Medic 2 doesn't seem as popular. Medic 2 allows you to essentially carry your territorial healing powers with you; units around a Medic 2 unit heal 20 HP per turn. In addition, in friendly territory, they heal 30 HP - an obvious numerical value, but in terms of Bushido, it's more relevant.

A normal unit is pulled out between 40 and 60 HP, simply because at that damage level, its combat power is already significantly compromised. It'll take 2 to 3 turns to heal to full combat power in friendly territory. As Japan, you can keep units out until they have 20 to 40 HP, and with a Medic 2 Samurai, still only take 2 to 3 turns to heal in friendly territory. In hostile territory, a unit down to 40 HP takes 6 turns to heal back full. A Japanese Army can heal a 20 HP Bushido unit to full in 4.

The upshot of all this is that Bushido and Samurai allows Japan to hit harder for longer with both ranged and melee combat units. Between Medic 2 and Bushido, Japan can hit hard for 3 turns whereas a Civ without these advantages can hit for 1 or 2; and then Japan heals up faster and is back for more earlier.

Siege promo is almost just icing on the cake.

It is notable that America can also gain Siege and Medic 2 promo out the gate with the Minuteman; and the Minuteman has an additional movement and sight bonus (from Manifest Destiny) on top to garnish the deal.