I bought Garry's Mod today since I had some money on an old card and I've had a mild interest in this game.
So I bought it and messed around in the single player until I saw it had a multiplayer. So I joined a server and noticed some textures were purple and black, and somethings were just big ERROR messages. 
I thought I needed Wiremod for this problem, so I downloaded it and installed it.
 
After that the problem was still the same.
 
Do any of you know what is going on?

Yep what billny said, I think Counter Strike Source and The Orange Box are a good place to start.

Missing textures. I have the same thing on Oblivion after I installed it this morning with a hundred mods and I forgot some of the meshes and textures.

@Twitchey:

No, you need to buy valves source games in order to see the majority of the textures. Im sure there are mods out there that would be okay place holders, but im not great with mods, so i wouldn't know.

You mean this Purple Stuff?

I've played a ton of GMod. The basic packs you should have are HL2 and the episodes, CSS, Day of defeat source and portal 1. I haven't checked about importing Portal 2 stuff. When you join a server online for MP there's a good chance the server use mods you don't have. GMod is generally a big mess of mods and there will always be something fucked up about it. I recommend you start with checking out maps on http://www.garrysmod.org/downloads/ then start looking into nukes and bombs and all the crazy shit you can do. The black and purple checkerboards are missing textures. If you get any error messages you can ignore them if the game runs at all. XD