Improved handling, Step By Step

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My wife's son has a 2007 Yaris. he wants to improve the handling so I'm going to buy some stuff for him and teach him how to install it.

I don't know diddly squat about these cars. We have a Miata that my wife drives as a DD and he likes that. Don't know if we can get close to match that in handling but would like to try.

He wanted to get new rims and tires but he's got quite a bit of life in the existing. I told him we may want to go sway bars first until the tires wear out but searching on here I see lowering, struts, coilovers, and a bunch of other ways to go.

I don't want to dump a bunch of money at a time on this thing. His birthday is coming up so I thought I'd get him something. I'd like to do upgrades on a step by step basis over time.

It is his only car but he doesn't drive a lot, lives close to his work.

What would be the first thing to do?

Thanks.