Frankly, I think you should look at them all. Scrum because it heavily emphasizes iterative and incremental development. XP because it gives a lot of advice on the technical side of development. Kanban because it emphasizes WIP limits and flow.
That's how I've come to know them anyway; I've noticed they've all influenced each other heavily over the years. In either case, no methodology has all the answers.
For me, a very important core idea for everything "continuous" (both continuous delivery and continuous deployment) is making things as small as possible: make the stories smaller, so they're finished sooner, which makes you focus on iterative, emergent development with quick feedback. But also make the components in your application itself smaller and more decoupled.
I.e. if you focus on small services that communicate with each other through some form of messaging, the services become easier to understand, easier to test, and there will be less chance of your changes inadvertently rippling through to other parts of your code.
For a more elaborate albeit more "extreme" explanation on the latter, here are 2 very interesting videos: https://vimeo.com/79866979, https://vimeo.com/74452550