A shorter sidewall will increase the handling due to less sidewall flex. Wider with the same size sidewall will help a bit as well.

 

Update. Purchased "Starfire" brand, 225 50 17 (the best upsize I could find in cheap tires) for $275/set. So far, 20,000 miles on them and they look good. My brother who works in the industry says "80% of all tires are now made in Korea or SE Asia, so if you're not going to buy high quality (Goodyear, Pirelli, etc.) then buy the cheapest you can." I checked various UTCQ codes, etc., but have read those aren't reliable anyway. Car handles better. Next set I will try a bit more extreme upsizing (235 45 maybe).