Best order for water filters to go?
The order you have your filters is the correct order. You don't need to waste money on chlorine filters to have better tasting water in your toilets.

If you think you need additional sediment filtration I believe you can find a carbon filter with better sediment filtration to use at each sink. Those housings also take GE brand filters and other filters of that size so look around to see if there's something suitable.

If you can't find anything you may want to consider adding an additional housing at each sink so you can have an independent sediment filter as well as a carbon filter. You can also try replacing your current filter housing with a 2 or 3 stage under counter filtration system that includes a separate spout for filtered water so you don't waste your filter media for things like washing dishes.