#1 Lower the nose, flat floor all the way to the tip of the car
This is my priority, those vulture beaks ruin modern F1 cars for me.
#2 Keep the nicely curved sidepods.
It has taken F1 designers 25 years to create something better than boxes, now we have a nice harmony between a freely flowing body and similarly shaped sidepods.
#3 No aerodynamic appendages (that is, keep the current regulations)
A sports car should look sleek.
#4 No frills front wings, just one plane that can curve only in lateral direction (i.e. cross section can be curved).
Of course this would be less aerodynamically efficient, worsening the flow over the rest of the car, but that is to the good. Less dependence on the flow => more overtaking, especially when coupled with #5. I also would not mind making the front wing smaller, but am willing to compromise.
#5 Wider tires
Every boy knows that powerful cars, trucks and bikes have big tires, F1 should be no exception. Increased mechanical grip would aid overtaking.
I guess I’d like the basic shape of 80′s to early 90′s cars refined using recent advances in aerodynamics to make them more elegant (less reliance on flat planes and sharp angles, something like the step from F-117 to B-2).
#6 Large car numbers
I second (or perhaps fifth) this notion. I can’t understand how one can on the one hand claim to strive to increase popularity of the sport and on the other hand make it increasingly difficult for viewers to tell apart drivers. This reminds me:
#7 Drivers’ helmets should have distinctive and easily recognizable patterns and every driver should keep the same pattern throughout his/her career. In special cases changes are allowed after being approved by an Internet poll of fans, but no more than once per driver.
Not really serious here, but I do fondly remember the late 70′s when I had a chart of drivers’ helmets that served me well for many seasons.