Newbie question about which neural network to use for smallest amount of simulations needed.

I am pretty much still a beginner with neural networks and all, but I am quickly making my way through the Java version of introductions to neural networks. I want to figure out which neural network type to use for a simple game where two AI shoot artillery at each other. The thing is, the AI cannot run any of their own simulations, they take turns launching the cannons and they get the distance of how far the cannonball landed. They also have the location of the enemy. This is only a 2 dimensional world. In the tic tac toe example for the genetic algorithm, there was a population of 200 chromosomes which wouldnt really be possible because that would mean 200 turns in this little game. The AI will take a few seconds to build the cannon design and then fire, they would have an error rate based on how far off of the target they were. The simulations are not next to instant like a tic tac toe game because they are virtually building the cannon on their own. I may be explaining this horribly and this might not even be possible for a network to learn so fast without at least a few hundred simulations. Im just a complete beginner and something like this would really help me on alot of other tasks I am facing as well. Thanks for your time!