One of the major differences from open to close loop systems is the price of pumps; to go from cast iron (for closed loop, with barrier pipe) to SS or bronze (open loop, without barrier) is generally a big jump in $$$. Typically in Commercial setting that is why they run PEX pipes with out barrier, they spend a few extra dollars on pump and put in the relatively cheaper pipe (with out oxygen barrier) -> think stadiums where they have tubing on the order of 100k linear feet or more.
I personally would choose a barrier pipe for this application, since more than likely the pipe in slab has a barrier on it already; I also prefer closed loop systems
In regards to pipe size, it would be hard to determine the size needed unless you know how much pipe you already have in the slab. However, I would put in the largest tubing you can afford - you run less risk when running water slow thru a larger pipe, then when you have to jack up a pump to get more heat/GPM out of a smaller line.
HOPE THIS HELPS?
NOTE We always love pictures
Its nice to see other peoples projects once in a while.