[alohasurftoad]

lowering springs are just that, for lowering. while handling may improve because they are stiffer, they work best when paired with better dampers that match the spring rates. since oem dampers aren't meant to work with lowering springs, especially really low, the ride usually becomes bouncy and handling performance degrades, prior to dampers failing prematurely.

i suggest Koni yellow sport dampers paired up to whatever lowering spring you use.

stiffer/larger sways will definitely improve handling but depending on what you get, they're not exactly cheap. if you DIY you'll save a lot because in labor cost, because the install requires dropping the subframe. not sure it's within your budget.

a front strut tower bar is a cheap easy upgrade to stiffen the chassis some.

swapping to better, wider tires or wheels and tires is also necessary for handling improvement. increasing the front tire width and grip will reduce understeer.

an LSD will arguably improve it the most however, it's not a cheap upgrade.

"you have to pay to play"

it'll never handle like a Type R. don't even try. just improve it to some level that you're happy with.