The most popular places to buy neoprene are Macro International
(pricing varies), Foam Order
($75.60 per 51" x 83" sheet), Seattle Fabrics
($4.50 per square foot), and Rockywoods Outdoor Fabrics
($12 per foot - 50'' in wide by the linear foot; or $50-$72 per full sheet).
The first thing you should know about neoprene is what it is, and what kinds you should look for! Neoprene is a family of synthetic rubbers that is used in a multitude of things for it's ability to stretch, protect, insulate, be abrasion-resistant, chemical-resistant, waterproof, and buoyant. It is the material that wet suits are made out of!
Neoprene thickness can range from 1.5mm to 6.5mm. You want to stay at or under 3mm. While some like the thicker 3mm material for more warmth and elasticity, most prefer the thinnest 1.5mm material. Most sewing machines can handle 1.5mm neoprene when certain steps are taken (see "Can I sew neoprene on my sewing machine?"). However 3mm or higher you may have to seek out an industrial strength sewing machine or hand stitch the material. Keep in mind that neoprene is buoyant, so the thicker the material is the more you will float. The most common thickness for making tails is the 1.5-2mm.
The type of neoprene you want to look for is fabric backed neoprene. The fabric backing allows you to put on and take off the neoprene with more ease. Also the fabrics come in a multitude of colors and give a surface that will take paint well. Make sure to get the fabric backing on both sides (one side will be the colored side). Smooth neoprene is very sticky when in contact with the skin, making it extremely hard to get on and off, and will not hold paint on it's surface. Therefore it is not recommended.
Neoprene is not only more durable, and gives other great swimmable qualities to one's tail (like insulation), but it also looks more realistic than a fabric tail! The material is thicker, so the appearance of legs and monofins through the tail is minimized!
Note that to save money on expensive material. You can alter the “basic tailmaking” process by cutting pieces out for the body of the tail, then cut the fluke pieces out separately and attach it later with a attractively shaped seam.