There's lots here about different cleaning and sterilising here on the forum - do a search for Starsan or Chemsan as a good starter.
At the beginning it's important to understand the difference between cleaning, sanitising and sterilising.
Cleaning- visibly clean, needs to be done as a first step with almost all equipment, sterilising will not work if there are deposits of stuff the bugs can hide in
Sanitising - what most people think of as sterilising, but is reducing the harmful bacteria and yeasts to a level that won't interfere with brewing - this is the level most people need to work at
Sterilising - as far as complete as possible removal of all viable organisms from something - only possible through prolonged boiling and even that isn't technically full sterilisation. More of an aspiration
Some things clean and near sterilise like VWP, but you have to rinse it off with water which sort of defeats the point to a degree - still it is good for deep cleaning plastic things.
Starsan or Chemsan - good for sanitising as a short contact but needs to be room temperature or warmer, it's effectiveness degrades quickly when used v cold - that doesn't mean the starsan degrades, only that it's effect is a lot lot slower.
Bleach - diluted - lots swear by it, but again you have to rinse really and that does get back to the VMP issue. As a short term measure though it can be fine.
Boiling - good for small things that do need to be as close to sterile as possible.
Your new kit, a good clean first with anything, even dilute washing up liquid will be fine so long as it's properly rinsed. Then you need a sanitiser - Anything from VWP, bleach or Starsan can be used, though the first two will then need rinsed as well.
Hopefully some help and happy brewing!
Anna