Solution:
Open Steam.
Open your Library.
Left-Click "Garry's Mod."
Right-Click the now selected, and highlighted, "Garry's Mod."
Press, "Properties."
Press the tab across the top of the aforementioned menu called, "Local Files."
Press "Browse Local Files."
Look at the top of the file explorer and press, "Common" which is the directory previous to the one you would be in once pressing "Browse Local Files."
Select the "Garrysmod" Folder.
Press Delete.
Press Yes.
Go back to the menu we had open earlier, press, "Delete Local Content."
Install the game.
Make sure you have Half-Life 2, Half-Life: Episode One & Half-Life: Episode Two, as well as Counter-Strike: Source mounted once you get back in the game.
If you do not have the games, you can still get the content here, and extract the folders into your garrysmod/garrysmod/addons folder.
Make sure you don't have a shit-ton of addons. Addons like error hider or non-compatible addons are going to break the game. Personally I have just under 500 addons but they are from the collection of servers I play on and are all compatible. That can be fine, and work, but something outrageous like 2000 addons or four addons that are all the same have been known to keep players from loading into a server, due to it creating such a mass amount of errors, or outright crashing.
Start a "Singleplayer" game on the "rp_apocalypse" map prior to joining the server.
Try and join the server.
Also,
check out this autoexec I made and the launch options I posted, it may help you further.
If issues persist or new ones arise, please reply to me here, on my support thread, or a PM on the forums. My Steam is also available through my profile. I won't be around for a few because I got school and whatnot to go to but when I get home, hopefully I'll have the time.
Good luck.