Well, this is a broad one so I will just do a run down for now.
1018 - This is your generic low carbon steel. This stuff is crap to machine. Rarely leaves a good finish. If you dont want to pull out your hair dont buy it!
12L14 - Free machining leaded steel. Machines like butter, leaves a smooth finish, considered to be one of the most easily machines. Rusts easy. Will not make a structurally sound weld. During welding the lead vaporizes causing porosity.
1144 Stressproof - This stuff is great. Its internal stresses have been eliminated and machines very well.
4000 series - Chrome Moly steels. Available in a PH (Pre Hard) condition which is good for shafting. I have had very good results in turning and milling. When welding you need to watch out for your HAZ.
Drill rod - Also known as silver steel. This is hardenable rod available in air hardening, oil hardening, and water hardening. It is supposed to be use for tooling and is ground to size. Many people waste their money buying this because they think it is very round. Its not. It is usually triangular in shape and cannot be measured with a regular micrometer due to the grinding process. (Note: To measure roundness you need a V-Anvil micrometer) If you need round ground shafting ask for TGP or TG (Turned, ground, polished). It is heck of a lot cheaper than drill rod.
Hot roll vs cold roll: If you plan on machining it get hot roll. Cold roll steel is formed to shape while the steel is cold with rollers. This creates massive stresses in the material and will warp all over the place after you take off the outer stressed layer. If you take a cold rolled strip and face off one side it will turn into a banana.
This is a piece of 4142PH in my lathe for my conversion to brushless servo for the spindle: