From my experience the greatest factor in what cause NM/VP costs is the 'Political Cost' of the general being passed-over. You can pass-over some generals who have low political cost with little or no cost at all. Although I've never seen an actual explanation I imagine that the actual cost of promoting over higher seniority is calculated by factoring the seniority difference by the political difference.
Personally, as the Union, I've learned to never even use generals that give me a hard time with promotions. Here's a list of most of the Union generals that cause you problems and early war generals you will want to promote:
[font="Courier New"]Name -------- Seniority/Political Cost
Butler*** --- 6/20
McClellan** - 1/10
McClellan***- 4/100
Lyons* ------ 4/3
Lyons** ----- 4/5
Lyons*** ---- 15/7
Sumner* ----- 27/3
Sumner** ---- 3/5
Sumner*** --- 7/5
McDowell*** - 9/15
Banks*** ---- 7/12
Freemont*** - 5/20
McClernand* - 11/10
McClernand**- 6/12
McClernand*** 10/12
Halleck*** -- 13/10
Grant* ------ 4/5
Grant** ----- 8/15
Grant*** ---- 2/25
Sherman* ---- 8/3
Sherman** --- 13/5
Sherman*** -- 18/7
Buell*** ---- 11/10
Pope** ------ 7/5
Pope*** ----- 14/7
Sigel* ------ 36/10
Sigel** ----- 9/10
Sigel*** ---- 3/10
Rosencrans*** 12/7
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McDowell will have to get his but kicked in the east a couple of times to get rid of his seniority and political clout, but that's not hard to arrange

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Sumner, is only a 311. You have droves of those in Washington, send one or two to Missouri and send Sumner Council Bluffs. If you use him with Lyons, he will gain seniority and when he gets automatically promoted in Feb '62, god knows why, he will probably outrank Lyons, who you will be trying to get promoted, making it harder to use Lyons at all and harder to get him promoted.
Sigel is a poor general, but if you use him and get him promoted, his values drop even further and seniority skyrockets, which will give you issues with 10PC. He's a training officer, just use him for that and be happy.
McClellan - If you've ever read anything about how much trouble McClellan gave Lincoln then I have no idea why you would ever want to do anything with him. Lincoln could not know in advance what he was getting himself into when he put McClellan in charge,
you do; plus he's one of the worst general in the game. Give me Heinzelmann over McClellan any day.
Banks, McClernand and Halleck are lousy generals, and except for the training abilities of McClellan and Halleck, are completely useless; they are never ready and if you do put any of them to any other good use and they gain seniority it will haunt you later when you want to promote somebody else. McClanrnand is a recruiting officer, he belongs in New York or Boston with a single militia regiment passing out brochures and smiling at the pretty women.
You may want to use Rosencrans and Buell in a pinch, but I try not to, though there are worse things; see immediately above.
I've heard people say to give some of those lousy generals, especially McClellan a couple of militia, sent them to get slaughtered and let him take the blame, but I find that to be too chancy and if by some freak accident, he still might gain seniority.
Tip: if you can get them to be besieged in a town somewhere, so that they are forced to surrender, because they are starving, I'm pretty sure they get captured and are removed from the game, although there is never a message saying this. But how to get the enemy to do you this favor is the question

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In the end, you probably will take some NM/vp losses in the beginning promoting the generals you know will help you. Just do it and suck it up. It will make your game much easier and pay good dividends later.