I'm getting back into playing modded Skyrim and I wanted to make sure I'm installing SkyRe with IA and IW correcly and understand the process:

First, I get SkyRe, IA, and IW, since those are the mods I want to play with. However, SkyRe changes vanilla weapon and armor values, but does not change values for weapons and armors added by mods like IA and IW. Therefore, I need to get the ReProccer to change weapons and armor added by IA and IW. However, just the ReProccer is not enough for some reason (why not?), so I need to also get the Compatibility and ReProccer Patches for SkyRe by Xathra. However, this mod also requires Weapons and Armor Fixes Remade, so I get that as well. While I'm at it, might as well get Xathra's Unofficial Skyrim Redone Patch, even though it doesn't make sense to me why a modder is making unofficial patches for another active modder's mod.

If I do this, install all the mods, activate all mods, and run the ReProccer, will I be good to go? Is there some other obscure mod I'm missing? And what would happen if I just went with SkyRe, IA, IW, and the ReProccer?

You are welcome. http://www.youtube.com/watch?v=LIeIex-ZbPE

ReProccing is complicated, you seem to be doing well at understanding it so far.

Without using the ReProccer patches your new armour and weapons will have unbalanced stats. ReProccer is automatic & rather heavy handed by default, and sometimes makes bad choices. Xathra's stats.xml goes a long way to sorting this out. I don't fully understand the logic behind Pre and Post reproccer patches, but it relates back to how the Reproccer file is automatically generated and will not be fully usable without some tweaks.

Skyrim Redone is "done" according to the creator, who recommends using the patch. He is working on a sequel rather than on SkyRe.