I would like to modify a WP Gallery to use the jquery cycle plugin by malsup. I know this is possible but would like to know best practice for this, if anything just pulling out the url for each image should give me enough to work with. Please advise on best practice for this. Note I do not want to use a plugin and would like to build this site on WP Core.
What your asking for has the basic functionality of a plugin, so saying you don't want to use a plugin doesn't make much sense.
Your template or whatever you wrap your info in, typically you want this in a loop to go through several images/posts or content.