If you ride SPD shoes, Buy Shimano MW-81 winter boots. They are waterproof with gore-tex lining. Water generally can only enter via the top of the shoe. Combine these with gaiters and you'll be very dry. I find these good down to about freezing and are great for spring / fall commuting or off road riding in sloppy conditions.
Also for SPD shoes in colder conditions, buy 45nrth fasterkatt or Wolvhammer boots. They are basically a cycling shoe with a waterproof bootie integrated in to the shoe. Fasterkatt is for moderate cold, Wolvhammer is for sub freezing weather. These are pricey, but very effective. Again, water can infiltrate through the top of the cuff, so gaiter covering the upper area will reduce the chance of that.
Shoe covers will help a bit, but most shoes are not sealed around the cleat and are very vented on the sides and may have water infiltration there, and will likely fill up with water if you step in even a shallow puddle.
Neoprene socks (look for ones called SealSkinz) are recommended by some for very wet and cold weather. You can wear these with normal shoes. Your feet may get a bit wrinkly, but it keeps the hot water in and the cold water out.
If it's not cold, then just deal with wet feet getting wet. Rinse your shoes when you get home and dry them out with newspaper, a hair dryer, or get yourself a fan powered boot dryer.
Wear wool socks as well, since if they get wet, they still retain some insulating ability.
For you legs, a downtube mounted grunge guard does a good job and can be installed and removed relatively easily and doesn't tend to get in the way of suspension or big tires as much.