i think what needs to be answered is tire width. on the s4 it comes with 18x8 rims and a 235mm tire. if you look at technical specs on tires for example toyo http://www.toyo.com/tires/tire_specsheet.cfm?id=18 the 235mm width is good for rims from 8 to 9 inch, 8.5 being optimal. so, how wide do you want to go for friction purposes? in my past experiences, my vehicles stock tire width shorted the max by about 20 to 30mm. and if you go to that max, the rubbing will happen on turns, with pos g's or on pot holes or bumps or all three.

 

That's all well and good... but please note that different manufacterers and different models will yield different diameters as well. If only it were so simple as the formula! But yeah, not all... say... 225/40/18's have the same diamter... usually close to 1/2" in difference from one end of the spectrum to the other.

When I bought tires for my golf, clearance was a huge issue... I needed 215/35/18's... and actually checked all the tire manufacters to find out who made the 'smallest' 215/35/18's. I ended up with the ventus k104, which sucked ***... but, even it rubbed a lot. Thank god I didnt get a bigger tire.

 

I thought about getting coilovers, but since this is going to be my girl's car, I think I want to go the most economical way possible. I was hoping to get some insight as to what brands will yield me the lowest drop.

 

19's aren't exactly "economical"... neither is finding the widest tire you can fit in the back.

You can buy a spring/shock setup... but who knows, you might sit too high, or too low.