Welcome.
Union or Confederate depends upon your preference. I have yet to see a reenactment ball become a battle because people were wearing conflicting uniforms...
You should probably wear a period white shirt if you have one and a cravat. Spats can dress up any uniform.
Also a waistcoat- if you don't have one don't unbutton your jacket all the way. At that time men's drawers were long and were generally worn outside of the shirt so they could be pulled up easier if they slipped down. In consequence in some pictures of the dead you see the underwear tops above the trousers and it would be HIGHLY irregular to allow a lady to see such a thing. If it was hot, a man was working, and there were no ladies about it wasn't uncommon to go in the shirtsleeves without a waistcoat, though. I have also heard that suspenders were considered underwear but I'm not sure on that one.
An officer might wear shoulder scales (US mostly) and other fancy regalia not normally worn in combat- as well as his sword, which is hooked up to the belt with an s-hook for the occasion. Spurs were sometimes worn to balls (such as Washington's Birthday in early 1864) but generally not as they would wreak havoc on the ladies' dresses.
Jackets are often worn not fully buttoned for formal affairs. The top couple might be left undone to show off your cravat. The middle few might also be unbuttoned (see image below, which is Pvt. Alfred Dolaway of the 56th NY, Co. F in 1861). This supposedly represented that you were subject to outbursts of emotion (why the unbuttoning is centered about the heart), which in those poetic days was looked highly upon. To support this you should also know quotes from Poe or Byron.
A confederate impression can be accentuated for the occasion with a secession cockade (don't wear one in battle, though except Manassas No. 1 &c.)
White cotton gloves are also highly advised. They make you look good and hide your sweaty palms!