Your runner will be subject to aerodynamic drag. The force of drag is basically this:
$$F_D\, =\, \tfrac12\, \rho\, v^2\, C_D\, A$$
Where $\rho$ is the density of air, $v$ is the speed of the runner, $C_D$ is their drag co-efficient and $A$ is their cross sectional area. If you double your speed, the force of drag will quadruple. When you push off against the floor with your feet, not all the force is going forwards, but some will also be going up. Sprinters are limited with how much forward force they can impart per stride without slipping, which is why they use spiked shoes for extra grip. To get double the speed, then, you'll need to more than quadruple the force your legs impart and you'll either end up springing much higher into the air (your "bounding gait", perhaps) or skidding on the ground. Firing yourself into the air is bad, because it will take time for you to come back down again (unless you have super-gravity-enhancing powers), time in which drag forces are continually acting to slow you down.
What you need to do then, is:
- Wear suitable shoes for super grip. Studs on grass (but you'll still be very limited on such soft surfaces), spikes for asphalt, grippy rubber shoes for hard, smooth surfaces. One shoe won't suit all purposes. You'll never catch a bad guy in a dune buggy racing over sand.
- Wear a highly aerodynamic helmet (like one of these, the sort that time trial cyclists wear), ideally with a visor because super speed bugs to the eyeball will put you off your stride. You may finally also have a good excuse to wear a skin-tight super-suit too, to keep your skin friction nice and low and try to keep your drag coefficient as low as possible.
- Get down low. Look at the pose sprinters are in when they start running. You'll be moving more like a conventional tetrapod, all stretched out, though your
forepaws hands won't necessarily be used nearly as much. Keep your cross-sectional area down to minimise drag.
So the answer is probably going to be: (c), neither of your two options but more like a low down speed scramble, whilst wearing a funny outfit and carring a bag of shoes.
ETA: if you've got super strong, super fast legs then the way to go really quickly is to get a bicycle, you know. Much more efficient, no worries about punting yourself into the air with each step or what shoes to wear, and with an aerodynamic fairing you'll have far fewer drag issues. Also, I don't recall anyone else talking about a super-cyclist before, so you could be the first!