We didn't do too many cabinet organizers. We bought bamboo organizers off amazon. One is a flatware organizer which is adjustable to fit different size drawers. The other is tension dividers which can be used on different width drawers. We did not use liner in our upper cabinets but did use Gorilla grip drawer liner in drawers to keep things from shifting.

I have several of the Uppdaterra flatware trays, and I really like them. For smaller drawers, I've used the Madesmart brand, which hold up really well, and Madesmart has different configurations for trays for gadgets and such, not just for cutlery.

I can also recommend Ikea's Variera shelf inserts, to add an additional level for storage. If they're the wrong size, there are lots of others, but I like their quality and price point.

I use these to store my pot lids vertically; this is a Canadian store, but I'm sure you can find something like it wherever you are

I also highly recommend that you get aftermarket pull out storage shelves for any cabinets you have (rather than shelves); I've used several different brands, but I like Trinity and RevAShelf - this is a Trinity one for under sink cabinets

I also have several of these in my cupboards around the house to help with storage, from SimpleHouseware

Edited to add: I agree that I never use shelf liner, but I do use a grippy liner in drawers to keep things from moving and getting noisy/damaged. I use Duck brand EasyLiner, and it can be washed and reused a few times before losing it's grippy cushion

For shallow drawers (flatware and utensils) I use Lee Valley drawer dividers, so I can completely customize.

Lee Valley

For vertical storage, I use Rev-A-Shelf U-shaped tray organizers.

Tray dividers

I have the Uppdatera peg boards in a few drawers and a couple accordion type organizers, also from IKEA, in another drawer. Have found both to be handy. (First pic is the accordion style; second is the peg board.)