Have not installed Mint for years but just run a install of Fedora 19 for work and disk encryption (work policy) was super easy. Just next-next-finish!
As far as kernels go just run the latest one available for the distro you want. If that doesn't work for you, and you need a bleeding edge kernel you can download and compile the latest without too much problems.
Lots of how to's on the interweb or find another distro with the kernel support you need.
EDIT: Fedora 19 current kernel version is 3.12.5, if that is any good for you? 2.6.39 is rather old now.
Info on whats in and out of the latest release here: Kernel Changes
Changes are gernerally hardware support and features like memory, power, cpu and gpu management.