First, congratulations on such a handsome piece of family history!
There is no sure way to determine regiment just from the sabre, (unless it had the regimental number or badging engraved on it).
Straight-bladed sabres are known as 'Prussian pattern' sabres.
They originated from the straight bladed swords carried by European heavy cavalry regiments. The most common Prussian-pattern Sabre in the ACW was the 1852 pattern, but there were others.
Pic: http://www.smkw.com/large/knife/CS88PSA.jpg (modern reproduction)
I would recommend you try here: http://www.americancivilwarforum.com/acw-forums/
Identifying obscure ACW memorabilia is 'business as usual' for those guys!
Your description of the markings reminds me of this particular sword, from the same site: http://www.americancivilwarforum.com/need-to-identify-a-civil-war-sword-133204.html
(That one turned out to be post ACW, but don't worry, that doesn't mean yours is!)
These types are Officer's swords - a straight-bladed sword carried as a mark of rank by infantry officers. In US service, they were often referred to as sabres, although technically, the type is known as a 'smallsword'.
Hope that gets you on the right track!