I'vs never had a problem with ST's. We just put a set on my friends bimmer with good results. i have also had them on other vehicles.
the sway bars will do a lot for for handling, they connect your lower control arms to a solid mounting object to help reduce body roll.
the stb's mount at the top of the strut mounts, sometimes even conecting to the firewall or a point in the trunk...some say these help reduce the chassis flex a lot...but its all personal preference imo.