All iPads that have cellular data are on a contract-free basis and you only pay for the capability to connect when you buy the iPad from Apple (and presumably all other sellers - even a wireless store).
There is no linking of the account that purchased to the SIM cards and you don't need any sort of credit check, subsidy or contract with the iPad Air.
The devices in the USA are tied to the carrier that you selected, so if you wanted to let your recipients pick the model they wanted, just buy them an Apple Store gift card (which is very different than an iTunes or App Store gift card) so that they can purchase the appropriate model. The only down side is they may choose to use the gift for other purposes so you might want to poll them to their preferred carrier or let them haggle a closed box return / exchange with Apple or someone on the street with cash seeking an iPad.