Welcome aboard!
I can shed some light on your questions.
All foam insulations off gas over time. EPS loses the least r-value, but it's not as high to start with...so there's that.
Extruded polystyrene (often pink board or blue board) has better resistance to water damage in the real world, and is physically more durable than bead board (EPS)
http://www.concreteconstruction.net/durability/comparing-eps-and-xps-insulation_o.aspx
Urethane foam insulation comes in a couple varieties, sprayed in place and rigid board. The modern versions are way waaay waaaaaay better chemistry and durability than urethane foams from 20 or 30 years ago. They get used in some of the toughest installed conditions anywhere, commercial roofs. Read about it here:
http://www.finehomebuilding.com/how-to/qa/durability-of-spray-foam.aspx
Urethane foams have pretty much the highest r-value per centimeter of any insulation, and the gasses they use for foaming agents to make the board are pretty benign, both to you and to the environment.
I will throw a caution in there about any kind of glass fiber insulation. It performs according to the specifications, pretty much only in the lab. In the real world, when the going gets tough (very cold conditions, wet conditions) it can lose 1/3 to 1/2 of it's rated insulating power.
Here's a comparison of mineral wool and glass fiber insulation:
http://www.greenbuildingadvisor.com/blogs/dept/guest-blogs/mineral-wool-insulation-isn-t-fiberglass
I personally really really prefer blown in loose cellulose, keeping in mind, it will settle 3-10% in a year. I just plan the construction so I can go back and top up the wall a year later, and I have great insulation, and cheap, and it words as advertised ESPECIALLY when conditions are tough.
Here's a comparison of those two products:
http://www.greenbuildingadvisor.com/blogs/dept/guest-blogs/fiberglass-versus-cellulose
Have fun and ask questions!