Minecraft – Sphax texture pack & Feed the Beast

The Technic pack includes Optifine, which has support for HD Textures included. Try installing the technic pack first over a vanilla (un-modded, un-changed) version of minecraft. Then put the texture pack in C:\Users\yourname\Appdata\Roaming\.minecraft\texturepacks (on Windows), you can also type %APPDATA% in the address bar in windows explorer and navigate to .minecraft\texturepacks.

If this does not work try following the instructions in the "If you have previously used MCPatcher" section of this Minecraft Forum post.

If you're able to upload individual mods to your server the Unhinged announcement post links to a maintained list of included mods.

A major virtue of Forge is that install order is almost never a problem when you're dealing with pure Forge mods. The mods themselves will have install instructions that should be checked in case there is anything special, but in general Forge jar mods can be installed in any order after Forge. Coremods and plain mods go in a folder to be loaded by Forge at launch, and don't conflict. Very few or none will be jar mods anyway, and order can't matter for the rest. What you have to watch for is ID conflicts in the config files.

Note that this modpack is intended to have customised configs to make it "hard mode", so once you've installed all the mods you'll still have to download the actual Unhinged distribution and consult/copy over the config files to properly set up your recreation of Unhinged.