Probably nothing can spoil your carefully crafted Civil War impression more than a pair of modern eyeglasses.  Unless you wear contacts, one of the first personal items you are going to need is a proper pair of spectacles.  If you need glasses for distance viewing, then you're going to have to go the more expensive route of having prescription lenses put into period-correct frames.  But if all you need are reading glasses, then you're really in luck.... because lots of period-correct reading glasses are still available from many sources, including Ebay.

The most popular style spectacle in use during the Civil War Era had oval lenses and straight temples.  These frames were machine made and sold in general stores and by traveling salesmen. Most cost $2.75 each but, some cheaper versions were on the market. The wealthy bought gold and silver frames from jewelry dealers. A few heavily engraved solid gold examples show up from time to time.  Eyeglasses made from 1833 through the 1850's were also used during the Civil War. Such frames usually have square or octagon lenses and are made from brass, roman steel, and silver instead of the hard steel commonly used in the 1860's.

The typical case of the period was made out of pressed paper and many have survived relatively intact.  Careful shopping can yield you a suitable set of spectacles and proper case as well.

Sliding temple spectacles were usually made from 1820 to 1850 and again after 1870. The later examples are usually finer made of coin silver or gold.  Turn-pin temple spectacles were made during the entire 19th Century. Those made prior to 1860 could have been used during the Civil War.

Avoid the above styles, such as 18th century heavy double-folding and the later "riding temple" (hooks around the ear) styles still used today.  Riding temples did not appear until improvements in steel technology made thin spring-steel temples practical.  Colored lenses were primarily worn for medical reasons, and "sunglasses" as such did not appear until later in the 19th century.

One very interesting set of period correct colored lens glasses you will occasionally find listed as "sharpshooter glasses" or "rifleman's glasses".  These were generally amber colored, and had frosted lenses with a small clear circle in the center.  Presumably, they helped increase contrast and improved the rifleman's concentration by blurring out everything except the target area.  They weren't likely used in general combat, but may have been used by sharpshooters during the war.  

One sure way to destroy your image is to pull back your sleeve and stare at your Timex when someone asks you what time it is.  The common timepiece during the Civil War was the pocket watch.

The nice 1865 Waltham shown at the right was wound with a key which typically was carried on the watch chain.  You can spend $800 or more on an authentic period correct timepiece, or you can drop twenty bucks (sometimes less) on your local sutler and get an electronic equivalent that actually is far more accurate and looks almost the same as an original from the outside.  Remember, the watch is hidden in your vest pocket most of the time, and only the chain is generally visible.

You're actually better off to search for a reasonably authentic chain.  Try finding a long-link, T-bar type chain similar to the one at the right and you'll be pretty close to period correct.