The Ubuntu Core officially supports Linux kernel version 4.4 therefore any new IoT device that is Ubuntu Core based should consider using it if possible. Moreover this is a long term supported kernel by the Linux kernel community.
Also, you could use an older version of the Linux kernel. Keep in mind however that some features might not be available. For example you need at least Linux kernel v3.13 to have the Bluetooth Low Energy functioning.
Using an older kernel yet having good interoperability will most probably require you to backport the Bluetooth part of the kernel from the newer release. This can be easily done using Kernel Backports Project
|KERNEL VERSION||SUPPORT STATUS|
|>= 4.4||Will work out of the box|
|>= 3.13||Ok for Bluetooth Classic and LE however consider backporting|
|>= 3.10||Ok for Bluetooth Classic however consider backporting|
The heart of Ubuntu Core is snapd which has some constraints on the kernel version used. In particular it requires the newest AppArmor patches. Therefore, when choosing a kernel please take a look at sample kernels that have all the bits necessary for snapd to run included. Also make sure to read the Board enablement overview.