I've reinstalled my game and I'm redownloading all my mods. I know Loot can sort the list but I'd like to install them in the order they generally should be. Any general advice about which sort of mods should be downloaded first? If you could show your sorted lists to use as a general template it would also be helpful.

Generally speaking, install order doesn't matter except for loose mesh and texture replacers. And in the case of the latter, start out with the general replacers (SMIM, texture overhauls etc.) and install specifics afterwards. Some mods come with SMIM etc. patches, so those patches should be installed last.

What Arkngt X said. I would add that if you use a good mod manager like Wrye Bash or Mod Organizer, you can easily adjust both install order and load order on the fly, so you don't need to worry about what order you actually install your mods.