First off as others have already said, Iowa doesn't have a FOID card. The easiest way to put it is that you can either get a permit to carry (concealed), or a permit to acquire pistols and revolvers-which is commonly referred to as a permit to purchase. A permit to acquire pistols and revolvers also enables you to purchase longguns in Iowa. This is kind of confusing because Iowa code 724, which is the chapter that deals with firearms sales and permits, doesn't state that you need a permit to purchase longguns, but says that you can purchase them if you have one. The permits to purchase are available from your local Sheriff's office and are $5. They usually take 3-5 days to get.(in Clinton Co)-there's a professional answer.
Personally I have bought two shotguns at Gander Mountain in Davenport and they asked to see a permit to purchase both times. I always thought that you needed a permit to purchase any firearm even though I couldn't find anything stating that in chapter 724.
My suggestion would be to get a permit to purchase. It's only $5 and it's good for a year so if a few months down the road you're at a store and see some gun you just gotta have your already covered.