Sharpshooters give a +1 initiative to every unit in the stack they are in. This is the only unit I have noticed so far with any bonuses of that sort. They might help a division in other ways as well by slowing enemy movement and opening fire at longer range.
I started off using my sharpshooters as lone bushwhackers, then I realized they could add a lot of punch to my divisions. In fact, I'm thinking every division should have at least 1 sharpshooter.
A wild idea that I haven't tried yet is a division full of sharpshooters. They tend to have 25 power/element which is about equal to a normal infantry regiment. The price also seems to be in the same ballpark. However they only have 250 troops per element, vs 1000 for most line infantry. I suppose this means they don't have a lot of staying power for repeated engagements.
My current thinking is that cav need to accompany a stack for detection, but they do not need to be in a division that is part of a corps. Similarly, I see no value in having cav attatched to infantry brigades. The strongest infantry brigades you can build have cav and artillery attatched. I'm thinking it makes more sense to buy everything separate. Some of the strong infantry brigades you are given have cohesion bonuses, etc. I'm not sure if you get a bonus on ones you build. So is buying everything separate a good idea?
My current ideal division for 1861 is:
1 general
1 sharpshooter
4 artillery (a mix of rifled and smoothbore types)
12 line infantry elements
BTW: I'm a complete rookie at this game, so if my thinking is askew anywhere please point it out.