When downloading, pay attention to the files you are grabbing. Please read all mod pages before downloading and installing mods.
The other issue I had was my own fault, forgetting to install a patch after downloading. The first issue was with a largish 'expanded territory/quest' mod that caused CTDs for me, presumably due to known conflicts with one of the DLC. I only had two real issues when testing out all of these mods (and a lot that didn't make it).
As a user pointed out in the comments below, Fallout 4 is a lot more forgiving when modding than any previous Bethesda game. This guide is intended to be a list of mods that work well together and enhance the Fallout 4 experience without straying (at least not too far) from the unmodded game, gameplay, and lore.