The Single Fin
The single fin has a smooth, neutral turning style. It is easy to turn and control, tends to be pivotal (due to one centered fin), and has a looser, freer tail feel depending upon the size of the fin. The smaller the fin, the looser it will feel, and conversely the larger the fin, the more "drag" (better for noseriding). The fin box allows for different sized fins as well as their placement. The box is more versitile than a permanently fixed "glass-on" fin for travel and for trying more options for size and placement of your fin. Start out with your fin in the middle of the box. Try it and then adjust it to your taste. Bring it back for longer drawn out turns and bring it forward for more turning.
The Regular Tri-fin
Unlike the single fin, the regular tri-fin utilizes a small center fin with two side fins to aid in stability. This gives the board a loose but positive "shortboard feel" The side fins help the board hold in for fast paced turns and vertical surfing. Fin Systems out there include the FCS plugs, FCS Fusion, FCSII and Future Fins. You can also Glass-on fins: Plywood, bamboo or glass fins which is a permanent placement.
The "2+1" is a good compromise. It has a Single Fin long box in the middle with 2 "side-bits" or side fins. It has the feel of a single fin but the control of a tri-fin. The two small side fins act as stabilizers. The size of the center fin will determine whether the board will feel more like a single or tri fin. The best thing to do is try all three and determine which fin set up feels the best for you.