If you wish to dress as a lady of the 1860’s, the full hoop skirt with a blouse and a wide ribbon sash tied in a bow in back is a very easy option. You can make the skirt as described by the first two websites listed below.
You can buy the skirt, a dress, or a skirt/blouse combo on eBay. These two are very nice and come in several colors.
With some luck, you can find a formal gown with a full skirt / crinoline at one of the thrift stores. If you add a cape or shawl, you can often create the correct period look. This is an easy and inexpensive way to pull an outfit together. You can also shop for vintage style accessories (cameo pins, gloves, etc.) at thrift stores.
Hoop skirts, crinolines, and petticoats can be found on eBay, also. One good quality shop with reasonable prices is listed below, but check the listings. Sometimes you can really get a bargain.
Remember that 1865 is just after the Civil War, so when looking up information on fashion, search Dickens era Ladies dress, Dickens era Gentleman’s attire, Civil War dress, Civil War gentleman’s attire, etc. Here is a picture and some more ideas:
For the men, A patterned fancy vest would be great, although any nice vest will do. If you own a pocket watch, it is a nice touch. A long sleeve dress shirt and a bow tie, ascot, or western tie are good choices. And of course, dress pants and shoes. You can go all out and rent a costume, too.