I vote Army of Immortals, for a couple of reasons.
First, as has been mentioned, getting that first army and a victory allows the building of Heroic Epic, which leads to more leaders, and is actually higher culture than Hanging Gardens, IIRC. It will also later allow the military academy.
Second, an Army of immortals is worth more than just a stack, for several reasons. The one vulnerability of Immortals is the lower defense, but an Army allows them to defend in turn, making it much harder to kill. In fact, the AI rarely attacks armies at all, in my experience. On the offense, an Army is a great city attacker. It often takes 2-3 attacks to kill off the first defender in a city. This costs a couple of units, and in the process the defender can get promoted 1-2 times, making them even stronger. The Army in effect allows 3 units to attack in sequence, and as long as the third one wins, all three units survive. As important, the defender does not get promoted in between!
This is especially true with the immortals. As our opponents get pikemen, the immortals will have less of an advantage, with defensive bonus it will probably not even be 50% chance against a city, but with an army, the extra hit points means it can still usually take out that first unit. The AI then tends to have only a spearman as the second defender, they are not as thorough with their upgrades.
Third, Armies make great garrisons when taking a city. I have often taken a city with my 3rd or 4th attacking unit, but since the others already moved(attacked) first, they cannot move into the city to supress the resistors. An Army that takes out the last defender, however, moves in with all three units, and it seems to supress the resistors pretty quickly. (I remember some debate some time back about whether the army counts as one unit, or three, or four, or just what, I know it counts as 4 for sea transport, and all the component units show up at the bottom of the city screen, in my experience it does quell the resistance quickly).
The Army should definitely be all immortals, I am not sure what the advantage of putting a spearman in the army would be, immortals already have a defense of 2.
If we do decide to go for a wonder, I would go along with Hanging Gardens, to use the leader quick and open the slot for another one. I think it is much to early to build the Forbidden Palace, and the American cities are probably too close anyway. If it is our destiny to expand throughout the continent, we will have a much bigger empire than we do now. But this is all the more reason for an ARMY, so our historians can write their great Heroic Epic, and inspire future leaders to come forth and answer the call!
Let them build our wonders!!