Check out a great article at
http://financiallyfit.yahoo.com/finance/article-113101-10286-3-toddler-gear-the-only-6-items-you-need
Hint: The six items she can't live without for her toddler are:
1- Car Seat
2- Crib (or once they're climbing out, a toddler bed)
3- Stroller
4- Sippy Cups
5- Potty
6- Crayons
Of course you'll need other basics like clothing and diapers. Make your own coloring books and flashcards. It doesn't look like she has any toys, but this article's author's child goes to daycare all day and has a lot of toys there.
As you can see, there's a lot she does without at home when they are home. She has her child use a salad fork and spoon while sitting on a regular chair at the table. She places a towel on her bed to change diapers. And they visit the library instead of collecting books at home.
If I had to list must have toddler toys, they would include a plastic doctor's kit in a bag, the ball you drop shapes into, some stacked measuring-type cups, and large mega blocks (we got ours in a handy truck). Make your own playdough and use pudding for finger painting.
Any other ideas?