I second keen sandals, which I try to find at consignment sales, thrift stores, or through Facebook marketplace. Or as a last resort, at REI when they offer 20% off one item. They last through multiple kids and are machine-washable. Crocs last through multiple kids, too.
We also provide rain boots (we walk in all kinds of weather to and from school) and snow boots (same) that I try to buy in gender-neutral colors so they can be passed down. Right before school starts we get sneakers (required for school, I try hard to find something with a textured, grippy bottom that works for hiking and outdoor play, not a slick gymnasium shoe), and soccer cleats ($20 at Dick's Sporting Goods, $35 when we got to adult sizes). I try to find all of the above used when I can, and will buy several sizes in advance. We've occasionally found cleats or sneakers at Ross/Marshall's/Burlington Coat Factory.
For girls, I've found some $8-$12 bargains on clearance at Target. Ask when their seasonal shoe clearances are, and buy ahead. They keys for little girls are colored sneakers, black dress shoes (white looks trashed right away), and a fancy pair of crocs that can be dressed up or down.
If you have higher quality shoes like keens, boots, or cleats with some life left in them, try to resell them for $10. Facebook marketplace has been my best avenue for that, although it may take a couple weeks.