What does "too fat" mean? do you mean too thick? Also, by "in far enough" do you mean the piston went ALL the way back in so the dust boot in nicely accordianed and the piston protrudes about 1-2 mm? Are the caliper slides frozen? with the pads off you can bolt up the caliper and move it back and forth with firm hand pressure, or you should be able to push the slides out with thumb pressure. Assuming you piston is really pushed all the way in, the caliper slides are free to float, and you mean the pad is too thick, then you have either the wrong pad or the wrong rotor. If your rotors have not been machined, the outer edge should still be near original spec. I have also seen many aftermarket pads that "exceed OE specs" by making the friction material thicker.
yes, a small amount of anti seize on the threads and some caliper lube on the slides is a very good idea. A bit if antiseize where the pad contacts the piston is not a bad idea as well for preventing noise.