I was born in Delaware (although I was raised in Alabama) and I now live in Maryland but teach in Delaware (including Delaware History). The input here has been excellent with lots of valid points being made.
Slavery was very weak in Delaware by 1860 with only 1,798 slaves in the entire state (less than 3% of the population). Only 2% of Delaware families owned slaves and they tended to be located in the southern part of the state.
Delaware was solidly pro-Union but generally anti-Republican during the war. Delaware voted for Breckenridge in the 1860 (45%) and McClellan in the 1864 election (52%) and local government was solidly controlled by the Democratic party in most areas.
The best sources within the State archives indicate that there were 11,236 white soldiers, 94 sailors and marines and a total of 954 black soldiers from the First State. A total of 12,284 Delawareans fought for the Union out of total state population (male and female) of slightly more than 110,000.
This number includes all branches of service: artillery, infantry, cavalry, as well as marines and sailors. Delaware contributed 9 regiments and 4 companies of infantry, 8 companies of cavalry, and 1 company and 1 battery of artillery to the Union army.
As a result of the Civil War, Delaware suffered nearly 1,000 in killed and hundreds more returned home wounded.
Per capita, Delaware provided more soldiers to the Union than any other state.
It is undetermined exactly how many Delawareans fought for the Confederacy. I have heard it claimed that as many as 2,000 Delawareans fought for the Confederacy, but I have never seen any evidence to back up such a claim.
It would appear that a more realistic number would be as few as 200 or so Delawareans fought for the Confederacy. As stated there were no “Delaware” units in the Confederate Army.
Geographically, Delaware would seem to be a "southern state" (i.e. part of the Delmarva peninsula) although is it also referred to as a "mid-Atlantic" state (along with Pennsylvania and New Jersey).