Mild steel will not be much good for making springs.
The correct material is Patented Carbon Steel Wire - sometimes called Piano Wire or Music Wire. After winding the coil around a mandrel of suitable diameter, the spring will need to be heat-treated at 250 degrees C for about 30 mins, and allowed to cool
without plunging into water or oil. (Spring Steel is used for springs made out of flat material, and usually requires hardening by heating to red-heat and quenching in oil, then tempering to 'blue' or 'straw' colour followed by air-cooling)
Note that there will be some change of size after heat-treatment - to make a single spring would take even an experienced 'hand coiler' several trial runs to get the sizes exact, so if you can buy a box of assorted springs and find one that does the job it would be a lot easier.
If you
have to make a 'bespoke' spring, and can calculate the force - or 'load' - at a couple of positions, you could use a program I wrote many years ago to find the correct size of wire, number of coils, etc. for the diameter needed.
It is still available to download on my old company's web site at
http://www.goss-springs.com/spring_program.html - click on the picture of a spring, and run the .exe file that downloads (You may need to download the VB40032.DL file also).
The program will give an indication of whether the spring is viable - i.e. whether the stress at each loaded length is within limits for the material, and whether the 'solid' length (when totally compressed) is less than the shortest loaded position.
The program also can calculate for tension and torsion springs.
I hope that someone might find the above useful, but if not, this reply gave me a chance to show off some of the knowledge I gained whilst working at a spring-making company for 30 years !