I am wireing up a 2 fuse box for a barn that will use lights only and a couple of outlets. Does the white wires that go to the light and outlets connect to the ground bar with the ground wires?

Unless this is a main panel right from a meter, which it is not, then no, the whites and grounds must remain isolated. The feeder to this panel must be a 4-wire, meaning two hots, an insulated neutral and a dedicated equipment ground.

I'd be very curious to see some pics of this installation.