I'm a big fan of Water Wizard. Its the original flocculant solution other then the good ole Alum. It is essentially the same stuff that water treatment plants use, Poly Aluminum Chloride, to remove sediment but in the right concentration for use in small batches. Comes with a couple of syringes (primary and a backup) and you just add one syringe worth to 5 gallons of water, stir vigorously and come back in 20 minutes. Usually helps to pour the clarified water into another bucket after the sediment flocculates and drops to the bottom. One ~$20 kit will do about 250 gallons worth of water.
I know Ed, the guy who owns Water Wizard, recently retired from his day job as a water treatment plant engineer, so not sure if he is still selling the stuff. The 4crs kit looks to be very similar so that would probably work really well too.
One note, I've seen reports saying that flocculants can foul up some water filters so you should probably check to make sure they are compatible with yours if you are filtering water. They work great for dish water though and really make a difference.