Let's start with a day to day task; dirty dishes. If you are lucky enough to have a dishwasher then you need to have quality dish washing tablets at hand to ensure it does a good job of cleansing those baked on messes. If you are hand washing your dishes, your cleaning supplies need to include rubber gloves, dish washing liquid, a soft cloth and a scourer. One of the more recent kitchen cleaning supplies innovations is the scourer on a handle which is a god send when you don't want to don rubber gloves but still want to remove built up food stuffs.
You might also need a bottle cleaning brush as part of your cleaning supplies to get to some of those deep crevices. And of course you will need tea towels to finish off the job; a good microfibre tea towel can save a lot of time and energy when it comes to drying dishes, particularly glassware.
Next you might look at the cleaning supplies required for your various surfaces; bench tops, cupboards, cupboard doors, drawers and shelves. Be sure to invest in a good spray and wipe type product with disinfecting properties as part of your cleaning supplies to ensure you are getting rid of any bacteria as you go. You will need a variety of cleaning clothes for this job depending what surface you are targeting. For example you might require a more abrasive cloth for your cook top spills but a soft cloth for stainless steel surfaces. Microfibre cloths are also an excellent investment as part of you cleaning supplies and are great for cleaning stainless steel and glass surfaces without leaving streaks.
Another key source of germs and filth is the kitchen bin. Your cleaning supplies should always include bin liners and you should clean down both the outside and inside of the bin using a disinfectant to kill off any harbouring germs.
Your oven can be a tricky one to attack; and not something that necessarily needs to be done particularly regularly. It is important that you refer to your oven manufacturer's handbook as some modern ovens so not require the harsh chemical bombs of old as their surfaces are more of a wipe and clean variety. You can also make preventative efforts by placing drip trays underneath where you are baking so that you only need to clean a component rather than the entire oven.
Lastly is your kitchen floor. After a good sweep with a broom, make sure your cleaning supplies includes a good, grease cutting disinfecting cleaning fluid and mop is required for cleaning.