What type of steel

I'm building a tow truck from a Wards/Gilson Gt front and a Cub Cadet Hydrostatic rear. I need to fabricate a 9/16" drive shaft about 3 feet long.Should I use hot rolled, cold rolled or drill rod. It needs to be machined just a little bit on one end.

4340 ? search for steels with torsion strength.

Use prehardened 4140. It will be about 35-38 Rc, should be ductile enough for a drive shaft.
Mcmaster Carr sells it.

That is pretty long for 9/16 rod, I would expect vibration. I would get 9/16 ID DOM tubing, for the bulk of the length and weld 9/16 rod into each end for coupling.

What RPM will the shaft be turning? If it's going to couple to the engine, turning up to 3600 RPM, I don't see 9/16 in anything being able to take that! Even lower RPM and high torque will be asking for trouble.

If at all possible, go bigger. The DOM tubing would be a good choice, thin wall, up around 1" or so. Bore to true the ends, pilot the end fittings, TIG weld to keep the heat down.

As others have said, the RPM your going to need is going to determine alot of what to use. If your turning a higher RPM, then DOM tubing with the ends made to work will be stronger, and lighter than a piece of solid stock. Too, it will be easier to balance, which you'd want to do if your turning a higher RPM.

Now if your turning below say 1000 RPM, look at the drive shafts for the PTO on most dump trucks. They are usually made from a piece of 1" solid, square stock. If you find one piece for the main part of the shaft, and then a heavy walled piece to slide over the solid piece, it will give you a little give from end to end, or simply get one of the square cut ends that they use and the shaft will slip inside of the end to allow that give.

At 3 foot long I would be concerned about whipping which is a function of RPM and not what type of steel. The torque you need to transmit would determine the size and/or type of steel. As some have posted going with a tube with a larger O.D. helps in both cases. The use of a center support bearing(s) could be used to address whipping if the O.D is limited to 9/16".

Remember, DOM is not pipe, do not use that. I get mine from metaldepot.com. I would also agree with the others that larger diameter is better You might want to get some 1" ID DOM and bar, then turn it down to 9/16 to fit in the coupler.

what is DOM dead old man??

Here you go,

(Drawn Over Mandrel). DOM Steel Tube is produced using uniformly high quality C1020 steel strip and is formed and electric resistance welded into its basic shape. After annealing to produce a uniform grain structure throughout, the tube is then cold drawn over a mandrel to give it these advantages: uniform concentricity around the central axis, better ovality, closer tolerances, denser surface, uniform wall thickness, and higher physical properties. The cold working process works the weld area to produce a sound, dense, and homogeneous structure comparable to that of the base metal. The weld line disappears, causing DOM tube to be virtually seamless. The surface is superior to that of regular seamless tubing, since the material has been cold drawn from strip steel. The hole is straight and concentric with the outside diameter. DOM Steel Tube may be machined, formed, welded, carburized, and subjected to other fabricating techniques that are ordinarily applied to low carbon steel. The use of DOM Steel Tube gives you a guaranteed micro-inch surface and lower productions costs by reducing or eliminating such operations as boring, honing, and finishing.