You should always wash your hands before touching any parts of your breasts pump and or pumping supplies.
The parts that need to be cleaned at each pumping session would be the membranes, valves, breasts shield (flanges),breast milk bottles to prevent the growth of bacteria and to avoid residue from your breasts milk.
Consider getting a large basin, one for home and one for work if you plan to go back to work. Never let any parts touch the sink directly, wash your parts in warm, soapy water for five minutes, then rinse in clean water, and place them either on a clean towel and a cool place when they are not in use.
When at home, dissect all parts of your breasts pump and wash with your basin.
There are also other ways to sanitize and or clean your pats once you are at home.
You can steam your breasts pump pieces in a steam bag......These bags allow you to disinfect within 3 minutes.
You can also use the boiling method- All you have to do is separate all your parts, fill the pot with water and once the water i boiling let the pump parts sit for up to 10 minutes.
Basin big enough to fit all your parts in
Towel for use of drying rack if you do not have any available
Steam bags if this is your choice of sanitizing method
Warm, soapy water
Place in a cool area after each use