Hi wishy.
It's always best to stabilize video at the source, i.e. use a camera with image stabilization, in some cameras you need to enable this function and that function might not be available at very high resolutions or at very high FPS. In my experience it's much better to downsize the resolutions to 1080p 60fps and get image stabilization enabled rather than shoot at 4K without any stabilization possible....especially if you're shooting kitesurfing footage while riding.
Post-stabilization is very easily done through Adobe Premiere Pro CC using warp stabilizer
I strongly recommend this software, it takes while to get used to it but totally worth the effort. Plenty of free tutorials around
Christian