What type of a rod should I use to fish ethernet cable?

First, long cable feeds only work if you already have tubing or possibly trunk through the building. Mostly trunk has too many sharp corners to traverses though. Other than that you can only feed cable in near straight lines under floorboards, and only then if there are no joists between your starting point and terminating point bringing the cable back up. Between floors you need to attempt to find fitted cupboards to take them up through, then box them in, or you will need to have a route under the stair treads. You must NOT run the cabling alongside any mains voltage cables for more than a few centimetres, or you can get VERY high inductive voltages along them. I have seen 110 volts or more between pairs from bad cabling. Destructive to equipment and possibly fatal to humans. You will NEVER get a very long run in one go. So you are better off using glass fibre rod kits which come in sets of 1 metre rods to screw together. The long flexible draw cables do NOT work without tubing. You do realise to do this properly you need to run 2 cables to any point you might require connections, all starting from the same cabinet? Otherwise you will just be wasting your time.