I'm trying to learn to skip jigs.

 

I build my own rods.

 

What should I be looking for (action, length, power) to skip 3/8-1/2 oz jigs with trailers?

Not even close to mastering this technique so I will answer only part of your question. Match the rod with  your height. Not the same as your height but choose the length that allows you to underhand skip without throwing completely side armed. This allows you to utilize your wrist more than your arm. 

 

This is something I just learned from watching Andy Montgomery and wish i would have seen it sooner

i would recommend a 6-10 to 7' medium fast or medium moderate fast with a good tip.  I like to skip 1/4 or 3/8ths arkey jigs with a large trailer like a beaver.  The larger the plastic with the least appendages works best for me.

Not sure on the rod maybe something on the shorter side but my reel would have letters SV stamped on it somewhere.

I be looking in to a 6'6 medium heavy. Right around 1/4 to 5/8