Regular road pedals are fine for 99% of track riders. The 6-day pro riders use them. Some hi-power sprinters use toeclips and straps or step-in (I hate the term "clipless") pedals with straps jerry-rigged.
I use Shimano Ultegra PD6610 and love 'em for our short, steep board track.
Unless you're a mega-power sprinter, road pedals are fine. I run mine with the adjustment quite tight - about the 3/4 level.
For a while I had the Speedplay Track Zero pedals (supposed to be a dedicated track pedal) but I hated them. I pulled out 2x and the was enough for me. They had less tension than my well broken in Eggbeater mtb pedals. Speedplay themselves didn't even want to take a look at them. Thank goodness for e-bay. Speedplay - you suck.
I'd suggest you use the same pedals that you use on the road but crank the tension up. That way you can use the same shoes.