So I would like to completely clean Skyrim of all mods I have because I want to start fresh. I want to do this because I have noticed that even though I disable mods and uninstall them and create new saves without them, there are still some scripts and what not left behind in my new saves.

So how do i completely get rid of mods for Skyrim and make it like I never had any? I am thinking I am going to have to uninstall and reinstall the game.

Simply uncheck all plugins in your data folder from your load order in the mod manager you're using and start a brand new character. It's a good idea to check in the data file utility that comes with the game just as a precaution. It will be mod free minus any texture and/or mesh replacers you may be using.

I do notice that there are still textures and meshes from those mods even though they are unchecked. But one thing I noticed was that I became a vampire and when I fed on someone it said I earned a new rank which is part of the Better Vampires mod which I unchecked and uninstalled. So why did it do that, and how do I fix it?

Also, I noticed that he does not have the red line going down his face that vampire's should have even though I got rid of the mod that fixed the line.

Steam has that "Verify integrity of game cache" feature which re-downloads any missing or altered files.
In the Data folder root, you should have only Skyrim.esm, Update.esm, the DLCs, and all BSAs which have entries in your Skyrim.ini (basically, everything with Skyrim - X.bsa).
Of the subfolders of Data, you should probably delete them all. You definitely should delete Scripts.
After that, run Steam's integrity check. If you accidentally deleted something which you need, it'll re-download that. But it's a lot less than a complete reinstall.

Thank you that is really helpful. I will see if this helps with my problem.