I'm not sure if there are any across-the-board "essentials" for toddlers, because kids each have their own tastes and needs.
Lili, my oldest, used to love crawling in boxes with a doll or two. She also loved to play with the same one or two dolls while hiding under blankets. As long as she had a "shelter", she was happy. She'd "invite people in", or "walk around her house", or check to see "who's there" when someone would "knock", and she loved that game more than her alone-time. (Of course, that changed when her brother arrived...)
Miles was especially fond of blocks, and he'd make whole cities, little houses, and fences, then he'd pretend to be a monster and knock them all down. He eventually focused on things like lining up his little animal toys (dinosaurs, safari animals, farm animals, whatever) in opposition to his cars (and there were a LOT of those), and then picking out different ones to "conflict".
Joseph loves anything he can stack, close, or open. His new favorite toy is my steamer container. He puts his blocks in there, and then closes it up, and then opens it up as though it were a present, clapping at his "accomplishment" of opening the top. He's not a "mouth baby", but we still made sure that everything we bought for him could be sterilized if need be (if other "mouth babies" come over to play, or someone in the house develops strep, etc.).
I figured that the kids would pass down their toys as they got older, but because none of their tastes really coincided perfectly, it's been the March of the Bargain Shopper. Walmart (as much as I dislike them) usually has very basic toys at very low prices, and going to second-hand stores helps a great deal. Plus, since my kids' ages are staggered with the ages of friends' kids nearby, we have the constant "toy swap" going on.
Invariably, children manage to accummulate a lot more toys than we'd expect. I'm not sure exactly how this happens, but it does. About once or twice a year, we go through all the toy boxes and throw out broken items (always happens), and then we bag up not-so-often-played-with items to either give to Salvation Army or trade with friends. It keeps their stuff fresh and interesting.
Only those that attempt the absurd, achieve the impossible.