A.J.
I always get one cheap version of every essential type of shoe each season.
Fall/winter for my 2 and 1/2 year old daughter:
1 pair dress shoes (little slip on flats of some sort). Got some cute glittery ones at Wal Mart $2.99.
1 Pair wet weather rubber boots (found some cute ones in sale rack at Old Navy $7.00),
1 pair of warm boots (found some cute ones at Target $19.00),
1 pair of sneakers (found some on sale at the mall $9.99).
Get a couple of pairs of tights so she can wear boots with skirts.
With these options, she always has the right shoe for whatever the weather, and whatever she's wearing, whatever she's doing. keep it cheap and simple since they only last one season!
For a boy, I'd do one pair sneakers (slip on style like Vans), one pair boots, one pair rubber boots, one pair dress shoes.
Good luck!