first off, you are running on the stock steel rims and tyres correct? the stock rims are 13"x5" and tyres are 175/70 R13 (i think)
I upgraded from this to wheels:15"x6" and 195/50 R15 tyres. there is an increase in handeling. i wouldn't reccomend going bigger than 17"x7" rims, as unleas you are prepared to do bodywork to the car, the wheels will rub (they may also rub on 16 or 17 inch wheels aswell, but can be fixed easily)
the bolt pattern for the 2000+ accent is 4x100.
if after you get the new wheels and you still want better handeling......get some lowering springs to lower the car (may cause you wheels to rub) and a rear sway bar. these would probably be the better ones but there are others like: performance shocks, eurothane bushes, front and rear strut braces, camber kits, caster kits and for the hardcore guys.....coilovers
hope this helps....

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