Mods are the top 25 most downloaded
Some of those mods are old and outdated. Not sure which off the top of my head though.
Did you install all the dependencies for these mods? Nexus should have a grey tab labelled 'Requirements' to link to the necessary pages. Also, some of the mods requure SKSE (Skyrim Script Extender) which is on a different site and uses a different install process.
Also, did you boot the game up before trying to start modding it? At least on Windows you need to do that first because the game generates some .dll files you need for it to work.
One more thing: which version of Skyrim did you get from Steam/GOG?
"Skyrim", also known as "Skyrim Legendary Edition" or "LE" for short, is a 32-bit game and is listed as just "Skyrim" on Nexus Mods.
"Skyrim Special Edition", also known as "SSE", and "Skyrim Anniversary Edition", also known as "AE", are the 64-bit versions, and mods for them are listed under "Skyrim Special Edition" on Nexus Mods.
Also, SSE and AE are the same thing, assuming SSE is updated to the newest version. The only difference is that SSE comes with 4 free Creation Club mods, while AE gives you access to "all" Creation Club content.
Long story short, if you bought the 64-bit version and are trying to install mods from the 32-bit version (or vice versa), a lot of mods won't work