I have wood planking in my 1946 home. the hardwood floor was directly on top of the planking. I would like to support the floor further with plywood but I do not know if I should use 1/2" or 3/4" plywood. The Planking is 5/8" so would 1/2" be sufficient I am on a tight budget. and 3/4" CDX is going for 19.00 a sheet right now. as opposed to 1/2" for 11.00 and I need 30 sheets so the cost is significant. Any suggestions would be a great help.

Thanks

1/2" will be sufficient. Just screw it down real good.

1/2 inch, screwed to existing subfloor, or rescrew existing sub, and staple the 1/2 inch. Suggest packing any low areas before installing plywood. Use craft paper or shingles for minor areas, something heavier if low areas are significant. High areas should be sanded flat before installing plywood.
The flatter you make the sub-floor, the more pleased you will be with end result.

ok great another issue I have is that i have a belly in one section it is pretty big 1 1/2" spans like 6-8 feet. My floor joist are in good shape and there is no rot. when I pulled the old floor up it was heavily shimmed in that area. I was thinking of using 3/4 plywood in the middle of the belly to bring it back up to height. what do you guys think

Thats a pretty significant swale. Have you checked for structural problems? Is it just sagging from age? You may want to add a support post under the joist system at that location, if possible.
But yes, you can use plywood to fill in the low spot, feathering the edges out to make a smooth flat surface.
Alternately, you could cut the existing subfloor out and scab sister joist(s) at the proper height to create a flat sub-floor.

well would the preferred method be to scab the joist with new ones and bring the floor to the proper height? And if so, what size joist would I use for 3 x 9 joist. I have used 2 x 10's for other structural work in the house but is it really necessary to use a 2 x 10.?

I would use 2X8's but I imagine even 2X6's would do, if properly fastened to the existing joists