I have a SQUEEKY subfloor of 1x6's on 16" centered floor joists on a 1957
built house. I planned on pounding down all the nails back down and adding
wood screws everywhere. I was going to install wood laminate flooring and
lineolium in different rooms. What material and what thickness of material
should I lay down first?

I've used 3/32" luan mahogany plywood. Ring nails at frequent
intervals, etc. Fill nail spots with concrete patch type caulk, and
smoothed out with a putty knife. Otherwise, nails will "print
through." To deal with the squeeks, use deck screws before you put
down the plywood. This all does raise the floor a tad, but I doubt you
will have any problems except where you run into a carpeted room.
There are some various wood or metal transition strips you screw or
nail in place. I have also used wedges driven in and glued from
underneath when I had a problem by the front of a refrigerator in a
kitchen where there was a lot of foot traffic and stress on the floor.