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Basically mods are compatible as long as they don't change the same core files or have files with the same name. Mods will often (but not always) list the core files they change. You can also compare the contents of the folders for different mods. If two mods have the same file name in the same folder, they are not compatible. (To do this you need to know how to copy and unzip the mods. You can probably Google instructions on how to do this).
As far as I know there aren't a lot of mod packs. I wish more people would do this. However I myself am creating a mod/super-mod/mod-pack that combines several mods that have to do with what I want to accomplish; on top of that, I am also adding some of my own material.
There are lists of popular mods you can Google. Many of these are compatible but you would need to visit the page and/or download them to be sure.