(I am in no way, shape, or form an expert on skincare.)
Face:
Cleanser: Cleansers can go a lot way. Just simply removing dirt and oils from your skin. (Try to find ones without fragrances.)
Facial scrubs: Facial scubs can remove deep dirt, dead skin, and oils hidden inside your pores. Try to not use them more than 2-3 times a week. Using them more than that can rip open your pores and damage your skin.
Toner: Toners can tone pores, remove makeup, remove unwanted oils, and cause puffiness to go down.
Moisturizer: Moisturizer is mostly seen as a must by most. Simply hydrating your skin and keeping it soft and supple.
Facial Oils: Oils protect your skin and trap the water and moisturize, keeping your skin hydrated.
Makeup wipes: Try staying away from makeup wipes. They are rough on the skin. (Try micellar water instead.)
Face Masks: Face masks aren't exactly necessary, but can help your skin in a small way. Try not to use them often.
Body:
Soap: Try using fragrance free, all natural soaps.
Scrubs: Scrubs can be effective in removing skin from trapped hairs, and removing dirt and oils.
Lotions: Lotions keep your skin soft and hydrated. (Personally I think baby lotions work the best.)
Oils: Using coconut oils or Vaseline (petroleum jelly) can be a great hydration boost and keeps your skin soft!
Perfumes: Perfumes are always great for an extra boost to smell fresh. Try to replace perfumes with essential oils!