Don't underestimate having them help out with chores - that can keep kids busy for hours - laundry, washing dishes, etc.
But in terms of real toys my child loves (age 4) -
From about 18 months onward the play kitchen was popular with toy dishes and food - to save money my daughter would use a lot of old tupperware, wooden spoons, and washed out containers (yogurt, milk, juice, etc. for "food").
Your three year old is probably ready for board and card games like Candy Land, Chutes and Ladders, Go Fish, and Memory.
For the one year old, I would recommend collecting smallish tote bags, paper gift bags, and boxes and letting him go "shopping." Have him collect anything - like a scavenger hunt - you can make this game more complex for the older one so they can play together.
Water play in the sink or tub is very popular at our house, so maybe a sand table?
And teach them to build a fort with sheets and empty boxes.
Also, Haba Blocks - basic wood blocks and architechural sets, and Tinker Toys for the three year old.
We generally try to stay away from character toys (like Disney). Look at Oompa Toys online, they have adorable European toys, that may give you some ideas (and carry teh Haba brand). www.oompa.com
Have fun!