I have an Amazon Gold carbon filter and water softener. It's not clear to me if the water main should go to the carbon filter first then to the water softener or vice versa. So, which goes first?
The filter can help keep the softener from getting dirty while the filter doesn't care if it gets hard or soft water. So I'd have the filter first.
Do you actually mean carbon filter? Or do you mean paper sediment filter? If it is a 1 to 20 micron paper sediment filter, I'd put that before everything in the house. Replace 1 to 4 times a year. If it is a carbon filter for drinking water taste, I would not put all my domestic water through that. Those filters are not typically designed for high volume.