You probably only need an FX-16, but a 23 is good for very soft mud. The 23 will be hard to set in firm bottoms.
You need 1/4-inch G4 chain. 3/16 is not enough. Used as a secondary anchor (kedging or as a V) you really don't need chain for chafe, since the boat is not swinging. 10-15 feet is enough, or even less.
3/8-inch rope (not rode--the rode is the entire rope-chain combination--calling the rope portion "rode" is confusing and is a pointless nautical flourish) is too small for an FX-23. 1/2-inch nylon. Length depends on where you will anchor. 150 may be a little short, because you need long scope for kedging and when using minimal chain.