Then certainly, cleaning your chain would be beneficial. More because it will give you a chance to check for any cracked links etc.
If you find you have a problem with your chain, the KMC610 is what most riders use with a single speed set up.
As for the rest of the bike, I just use fairy liquid to clean off any dirt and grime. Its as good as any bike cleaning degreaser solution you'll get. Plus you can make a rocket once its done.
I give my discs a clean first before using the brush/sponge/cloth on any other part of my bike.