Not sure how long your commute is mine is between 2 and 15 on country roads so I have a homebrew kin bright light up front for being able to see and a single flashing job for being seen. out back I have 2 blinky lights and 1 steady.
Mud guards IMO don't bother as if its piddling down you'll get wet anyway I have water proof shorts (don't mind wet legs can't stand a wet arse) Knee Warmers, waterproof socks, waterproof jacket. Fleeces, Hats, windproof gloves as required. Good waterproof bag or panniers