It is one week ago today that I built my new gaming PC, and I have still not been able to play Skyrim. It's not because there is anything wrong with the game, the mods, or my computer, it's just what I am doing to install them I guess.

I can't seem to be able to get my mods installed correctly by the time I have them all shoved in the data folder. By the time I have all my mods set up, there is always an error, Z-fighting issues with distant mountains, stuttering that wasn't there on the base game, etc. The game has just been a wreck. I have cleaned out my Skyrim folder and re-verified the files through Steam about 20 times now (cleaning out all my mods to start over).

Clearly what I am doing isn't working. So my question is simple, what is the proper way to install a bunch of mods without getting problems?

First I'd recommend using Mod Organizer, so you can easily toggle mods on and off without having to delete/uninstall them. Secondly I'd recommend reviewing the compatibility sections of the mods you use. Thirdly I'd recommend to not install many mods at once, but rather one or two at once and then go ingame to see if anything is wrong. Fourthly I recommend using BOSS if you aren't. Fifthly I recommend using Wrye Bash in combination with Mod Organizer to solve inherent compatibility issues between mods.

The Z-fighting is an engine issue.

The stuttering may be as well.

For installation, I prefer Bash.

I've no idea what you're doing, but as long as you're installing with at least the Nexus Mod Manager or Wrye Bash, using BOSS to sort your load order, and not installing wildly conflicting mods, you should be fine.

Step 1: Unzip or otherwise unpackage the mod from its compressed state.
Step 2: Go to your Skyrim directory in STEAM.
Step 3: any proper mod should have an ESP and several folders, labeled like meshes, textures, sound, etc. Check the readme, just in case the mod has a unique way of installing. A telltale sign is the absence of those folders.
Step 4: Dump everything into the Data folder. If prompted, hit "yes" if the computer tells you that there are folders sharing the same name, and any files sharing the same name will be overwritten. Very rarely will there be a case of one or more files overwriting what's already in the folder.
Step 5: Enable your mods from the launcher menu, under "Data files"

Bugfix- If there are issues, manually disable your mods under "Data Files" one by one until the problem is resolved. If the problem is not resolved, and persists despite running without mods, there is an issue with the game that may or may not be fixed later; in this case, make sure it's patched (it should be by default) and check to see if the Unoffical Skyrim Patch fixes your issue.

As has been said, Z-fighting is related to the engine (but perhaps partly also to your hardware, because not all players have z-fighting. Some users, however, have reported z-fighting showing up after installing mods). This is the major thread that covers the problem, what we know about it and what can be done: http://www.gamesas.com/topic/1336456-mountain-flicker-z-fighting/

Other than that, don't install conflicting mods and use BOSS.

Z-Fighting can't be fixed period. The INI file edits are questionable, since they cause extremely long loading times with some mods.