On the street is a complete sh*t show because you are never in control of the surface. There will always be fine sand and dust around. The biggest thing you can do for improvement is tires! You can see if you can find a softer compound tire i your size acceptability, but 245 is the smallest id ever want to go. You should also allow yourself to use 255 incase there is a compound available that you want. 10mm is not noticeable.
Im not sure what you are doing (driving style) whether straight or turns where it gets scary, but its possible you need new shocks and a suspension refresh. In my clapped out malibu suspension, that bottoms out and bump steers, needs alot of correction at WOT or gentle fun manoevres. Its very unpredictable. My buddy's regal with a hotchkis TVS and bilstein shocks is on the stiffer side, and although it has no traction also it is VERY controlled and very predictable. You can hold a nice long slide with some decent angle in that car at high speed and not get afraid. Unlike the malibu which will scare you at 40mph.
All this to say, you can only get so much traction on the street. Start with tires. Then do the typical dragrace geometry mods which load the tires from axle rotation, ie: LCA relocation brackets, antiroll bar, etc.. Then concentrate on the FRONT suspension to make the car more stable and stiffer. Basically new shocks, springs, steering components etc... Your problem here is the car is scary, and that the car doesnt hook. But traction is not solvable without electronics or slicks. So traction shouldn't be the focus, stability should be.