The three qualities that I look for in a backing board are:
1. It should be strong enough to hold the nails when they are under the tension of the string.
2. It should not be too heavy since it is to be hung on the wall.
3. It should be readily available locally.
I guess that point number three will be the main determining factor in what you use. The first place to look is around the house. Maybe in the loft or the garden shed to see what off-cuts might be available.
The next port of call is the local DIY store. If you can find a material that is already the size you want to use then you are on to a winner. I have used 12 x 12 inch cork floor tiles. These are quite thin so I sandwich two or three together so that the nails can be knocked in a reasonable distance.
If you do not find something the right size then the next place to look is the flat board section. Begin by looking for the lowest price material. In my local store this is quarter inch MDF (Medium Density Fibre) board. It comes in various thicknesses. I have used 10 mm (about 1 /2 inch) thick with success. MDF board is easy to cut with a wood saw. Better still if your local store has a cutting service then get them to do it for you. They probably have a large power saw that will cut it very accurately.
Other sheet materials to consider are plywood and hardboard. If it is thin you can always layer it to get the required thickness.