RE: what type of solder to use
If you had included a picture of your solder joint I could tell you if it was good or not.
All that you need to achieve is for the solder to 'wet' onto both pieces that you are soldering.
If the solder has 'wetted' onto the steel then the electrical solder is plenty strong. If the solder is just a blob sitting on the steel then the solder joint will fail because the solder did not actually bond to the steel.
If the rod is plated the electrical solder should easily 'wet' onto it, if it is a hardened unplated rod , you can solder it with 63/37 or 60/40 electrical solder but it is easier (especially for a novice) to use the Stay-Bright solder kit.
Its not so much the solder that makes the difference as the flux that comes in the 'kit'.
The flux that is included in the 'kit' is an acid and is much more aggressive than the electrical resin flux.
If the rod is not plated ... clean the end that will be soldered with sand paper until all of the quenching oil is removed, the steel should be shiny metal vs black.
Getting rid of that oil is key to getting the solder to wet to the steel.
Just use your regular soldering iron along with the flux that comes with the Stay-Bright and it should be as easy to solder as copper wire.
Someone mentioned rust earlier... you need to clean the soldered area with alcohol and then with water, the flux is acid and if not cleaned off will cause corrosion.
If you clean off the flux rust should not be an issue.
Do not use the Stay-Bright flux on copper wire, it will corrode it.