Whaaahhhh! Lots of confusion about Teckels....cute pup, by the way.
"Teckel" is simply another German or European term for dachshund - which is German for "badger dog". Call 'em weiner dogs if you want, but please don't call em "Doxies"...
Specifically, I think amongst the hunting community in the US "Teckel" has more come to signify dachshunds bred for hunting traits. In Europe that USED to be one and the same - they were bred for hunting and that is what they were used for. Just like other breeds, though, now a large percentage even in Europe are not hunting dogs anymore....think Labs in the US - some still hunt, but most do not. Just like any other hunting breed there is a hunting registry - DTK - "Duetsche Teckel Klub" for instance in Germany - but again just like any other hunting breed some folks focus more on field trialling than hunting.
There are 3 coat types - smooth, wire, and long. Smooth were the original dachshund, wire and longhaired coats were developed later. There are 3 sizes - standard, "rabbit", and mini. Generally the "hunting type" are standard sized - that is around 16lbs for females, 20lb for males, but other sizes can certainly hunt.
Mostly people in the US have only heard of wire dogs, because the Jeanneanys in the Northeast that were some of the first in the US to import dogs have used wires and that is where most of the info came from. Coat type has nothing to do with the ability to hunt - it is all in dog's bloodlines.
Wire dogs can come in a variety of coats - true wire, wooly, smooth etc. I think the "requirement" for a wire dog is the "mustache" hair on the face (I'm not 100% sure on that one, though). Your pup looks like a "smooth wire" to me if it came out of wire-haired parents.
Wire dogs are typically "wild boar" coat color - again there can be variations. Other "normal" colors for smooth and longhaired dogs are black and tan, brown and tan, and brown fading to beige. More recently some folks are breeding for color (ie white/piebald etc). Purists don't want color, and in some organizations you cannot breed with a dog with too much white on it.
Teckels are mostly used in the US for blood tracking, but I know of folks that hunt coons, retrieve ducks, and of course hunt underground (mainly bolt foxes or hunt groundhogs here in the US) with them. And if given a chance they may reduce the number of neighbor's cats in the area
Finally, have fun with your new addition to the family - weiner dogs have so much personality and have a tendency to be freakin' smart (we think moreso than the owners, around our house!). you have a 200 lb dog attitude in a 20 lb package. Look into Shaun Webb's posts, I recall his little sweet "Graetsche" jumped on a wounded pig in Texas, and our Oskar likes nothing better than to get ahold of a wounded deer while it is still kicking.
R