Electromagnetic Coil
The classic core is iron wire (or very mild steel) in a bundle. Much better than a solid core. They were dipped in varnish then wrapped in paper. Nothing wrong with doing that now. I don't have a number for you but as a ready source, I buy iron wire in big rolls at garden or hardware stores. It seems to weigh a couple pounds. I recall it in tool/cement working sections. (If you want to go faster, use the wire used by construction people to assemble rebar. It is thicker and a lot harder to bend. it won't work as well.) Stretch out a long piece like 10 or 20 feet and tie it to something solid. Pull on the other end until you feel it yield. There is a point where you feel no stretch and with a little more force, it "gives". If you pull much more it will break. It "yields" when you exceed the elastic limit. The wire takes on the new shape and will stay very straight. You can cut it into equal lengths as needed. If I need a bunch, I store lengths in a cardboard shipping tube. You may need some leverage (or a car) to pull hard enough, and do it with the wire supported by a table or on a flat floor. (This works with copper wire too and it gets a little smaller in the process and will slip out of the insulation if you want it bare. I do this to get nice wire for bread boards and stripping the ends is very easy. Worth experimenting with.)

I have used the plastic spool from anything like wire or fishing line and made a core to fit. You can get enameled wire for windings easily enough. The current and number of turns determine the magnetic field strength. There is nothing in the equations about keeping it perfectly aligned while winding. I like to keep it neat, but not gaudy.