Minor quibble. The 3100 is the lowest current appliance. The 2200 should also be able to run full GAiA.
The 3100 and 3200 use Intel Avoton (Atom C2000-series) chips. That family has a bug known as AVR54, which affects the Low Pin Count (LPC) bus. This bus is used to connect the processor to the system firmware. Eventually, it degrades to the point the system will no longer boot. Intel fixed this issue in the C0 stepping of the Avoton chips. I don't yet know if the 3100 and 3200 use C0 stepping chips.
Of course, throwing a hypervisor on a NUC and running firewall and SmartCenter VMs is my preferred option. I'm currently really enjoying SmartOS. NUC models are listed in the form #i#___, where the first # is the processor generation and the second # is the processor family within the generation. For example, the NUC6i3 has an i3-6100U processor. The three _ characters are letters indicating other capabilities of the device, such as whether it has a 2.5" drive bay or not.
The 6i model NUCs all work with 64 GB of RAM if you can find 32 GB SO-DIMMs. That's enough RAM to run a pretty sizable lab.