As far as I know, the only economic statement he ever made was "give to Caesar what is Caesar's" when asked about whether it was right to pay taxes or not... (Luke 20:20-26).
He did not have a lot to say about economics per se. But what about his teachings? His actions? What instructions that he gave to his disciples and to others would indicate how he viewed society?
OK ok, I won't give a short answer this time. The tough part about it is that the Achille's heel of any economic system is the same all across the board, and Jesus was surely aware of this: human beings. So long as there are corrupt individuals, there will be problems in economics. On paper, communism sounds great: a classless, stateless system where every individual is given exactly as many goods and services as s/he needs. In reality, we had the Soviet Union. Corrupt gov't officials remained rich, while the working class was dirt poor, having to wait on heavily rationed commodities, and since they knew they'd get the same pay no matter how much they worked, there was little incentive to work hard.
Capitalism works better, I think, in part because it assumes people will be selfish. So long as the market is free and supply/demand is left to work it's magic, and there is
active competition everything works great. The government would step in where it needs to (laws against monopolies; see Standard Oil), and otherwise let things go as they will. Problem is, we have a (very) corrupt government that's looking after the interests of the large corporations, instead of the common good of society; e.g. giving GM--a company that was doing badly BEFORE the recession--big bucks so that they can keep running their crappy company poorly(sounds like communism there, actually...), rewarding bankers who screwed over our economy by being greedy instead of having passed laws to prevent it from happening in the first place, etc. Meanwhile passing laws that interfere with normal supply and demand in ways that are unhealthy for the economy, such as paying farmers not to grow food to artificially raise food prices, etc. (I'm leaving out some because I don't want to spur an off-topic debate).
Socialism's main goal is to have as many people as possible (preferably everyone) involved in economic decisions. The way most of our elections go, and the most common intelligence level of Americans, I think it's a very bad idea. However, ideally, if everyone was educated and researched their decisions before voting, it could work well. I also like the idea of mixed capitalist/socialist economy where business are generally free to do as they see fit, but with some kind of fences set up so they don't wander into stupid territory, such as subprime loans.
tl;dr version, I have no idea which system Jesus would support. I think he would want a system where everyone was treated fairly and had opportunity to voice their opinions, but at the same time, he would know that people are corrupt, and very bad things can happen if any one group or set of groups (think the circle of evil of healthcare: doctors, insurance, pharmaceuticals) have too much power.
Really, I think that the ideal situation would be for society to follow the examples seen in Acts, where all are committed to helping those who are less fortunate themselves in the best way they can be helped (i.e. not necessarily throwing money at them). But, that was a small subset of Roman society, and such a subculture hasn't existed since then (to my knowledge).