Welcome to the forums Al
I think the simples answer is, build divisions. They are the backbone of this game. If you look through the forums--also the AACW forum, because CW2 is the evolutionary child of AACW and nearly everything written there is still valid--you will find numerous threads on what a division should look like.
My quick take on divisions is:
You can start building division in October '61.
They contain up to 18 elements, including the division commander.
My personal mix is:
1 Commander
2 Cavalry
1 Rifled artillery (10lb-er)
3 Smooth-bore artillery (6lb and 12lb-er)
1 Sharpshooter
10 Line infantry[SUP]1)[/SUP]
Early in the war, before you can build divisions, if you build along these lines, once division can be built, you may have less of a task in building balanced division. Don't worry about it if in Oct. '61 your divisions are not immediately balanced out. Just work on balancing them as you go along.
You cannot form corps until March '62. Until them you have only your army stacks and probably some corps-like stacks with a either a *** or ** general in charge. Especially the army stacks should have at least a Field Hospital in it. A Signal company will add 1 CP to those stacks and an Engineer will decrease greatly the time needed to entrench. Pontooneers reduce the time to cross major rivers, so I find those the more important in the West than in the East, but it mostly depends on where exactly you are fighting.
Once corps formation is allowed I always try to have those 4 support units in each corps, but I think the Field Hospital is the most important to start with[SUP]2)[/SUP].
Beyond that, loose cavalry is very important in the Trans-Mississippi and Far West, but in those areas having stacks smaller than divisions with infantry will also be important. There's no rule of thumb on this other than that you should always try to have your stacks well lead, but will never manage to do way in the West.
Cavalry will also always be important for scouting and chasing pesky partisans, even in the East.
Where you can build which types of brigades you will learn pretty quickly. There aren't actually that many different types.
The rest is experience, which you'll pick up along the way. But never feel that you can't turn to the forum to ask questions.
[SUP]1)[/SUP] You get a number of Elite brigades during the game. Many contain only line infantry regiments with the Strong Morale

ability, many also contain a sharpshooter and artillery. It is good to fit 1 of these in each division, because they add their Strong Morale ability to the entire division.
[SUP]2)[/SUP] I almost forgot, there are also HQ Support Units. These combine a Field Hospital element with a Signal Company element and have the Master Trainer ability added. The Mater Trainer ability gives each element in the stack 1 experience point per turn in which the stack does not move. Having them in your largest corps stacks is good.