The Red Baron
From: Adirondack Mtns, NY
I'm on my 4th run through Sibley's campaign as the Union against the AI on recommended settings. Just like you I'm playing the scenarios first to learn the system; this is my first AGEOD title. The first three times I played the scenario itself; this last time I'm fighting in NM again as part of the West campaign.
You need to capture El Paso and , ultimately, all your efforts should focus on that goal.
Colorado: As soon the Colorado Reinforcements unlock, move them south into NM. It will take several months between the inclement weather and terrain to reach NM and you will most definitely need them to nab El Paso. I suggest moving them one region at a time, from structure to structure, in passive mode so they can rest up along the way. The Indians and the CSA never seem to make a ploy for Colorado, the gold mines or northern NM at all; all the action is down south.
California: Like Colorado, as soon as the California Column unlocks, head south. You need to capture both objectives in AZ then head east to unite with Canby's and Carson's forces for an assault. Be prepared for a frustrating experience: between the bad weather and Carelton's inactive status, it could take you several months just to reach Western AZ for an assault against Pinos Altos. Don't forget to garrison your AZ objectives; otherwise, Indians will simply recapture them once you leave.
NM: I usually move Carson south as soon as possible. Canby's forces need to draw replacements while they wait to unlock. As soon as Canby and his forces are ready, I enable divisional command for him then try to smash the Confederate fort in the southwest corner of NM to kindling. The stockade acts as a accumulation point for CSA supply and can supply CSA forces in western AZ, making Carleton's job there much more difficult. If you can combine Carson's and Canby's forces to do this, do it, but don't wait. This will discourage J Baylor from moving west into AZ. If he does, or his stack is already there, you can still try to destroy the fort, which should bring him back east. You'll want to hit El Paso from the same side of the Rio Grande, not across the river. Capture the fortified town one region to the north to use as your base of attack against the city.
El Paso: I usually build 1 large division with Carson in charge and Carleton or Canby providing CP assistance for the stack. Pack everything you can into the division, but leave a modest reserve under command of your other leader for contingencies. How you attack depends, of course, on what Baylor and Sibley are doing. In 4 times I haven't had the scenario play out the same way twice; it has good replay and instructional value. In my current game I hit the city with Carson's stack at 512 against Sibley's stack of 200 sitting inside the defenses. After 2 battles in the same turn, I inflicted 3500 casualties, twice what I suffered, and lowered his CP to 40, but Sibley still holds the city. My CP has dropped to 135 and J. Baylor sits across the Rio Grande resting up from his march from Pinos Altos. Carleton is mired in Tucson; so, I have some tough decisions to make.
Builds: I usually build a NM militia unit to take over for Carson once he leaves his post in northern NM. You will also want some mounted NM volunteers + Rangers and cavalry for their scout/patrol value and to assist in the assault on El Paso. I usually build one supply wagon in CA and use it to erect a depot in the Pima villages. You could build more, but I achieved total victory with the stock forces and the few builds mentioned above; just husband your resources and attack in strength. You can build some CA militia and use them for garrison duty in AZ. They suffer a penalty but I have yet to see the Indians attack. They usually entrench and interrupt supply from CA. Speaking of supply...
Time is of the essence. Don't dawdle; hit El Paso as soon as you're ready. The Indians usually block supply from your CA depots, so your NM supply slowly dwindles. It usually takes 50-75% of the scenario before I'm ready to move against El Paso. By that time, capturing the city (and its depot) starts to become a necessity and puts the pressure on. Bringing Carleton's force into eastern NM is key to ensuring victory.