i don't want to sound disrespectful, but i felt it in the best interest of the readers to say something.
there are many inaccuracies in this post as well as follow ups. a lot of arguing by people with little knowledge or experience on the matter. just because they were taken from another source or because a reputable source did not correct inacuracies does not make them right.
there are literally 100s of breeds of goldfish most of which are not know in the west. anything you can breed true is a breed. the cross between breeds is called a sport. sports do not breed true. a sport is the goldfish equivalent of a mut. they may be cool but wont produce offspring that are consistent in their traits. a breed starts as a sport or a mutation and the traits are stabalized over time through line breeding (inbreeding) just as with dogs, cows, horses and all other domestic animals. just because you don't know the names of the many breeds, does not mean they don't exist or they are not breeds. this post lists a fractional percent of the many breeds. within what westerners would call ranchu there are probably a a few dozen or more breeds. there may only be subtle differences, but the differences breed true. lionhead, buffalo head, lionchu, black ranchu, top-view ranchu, sideview ranchu, edo nishiki (calico ranchu), osaka ranchu, isumo nankin, eggfish, phoenix eggfish, blue ranchu, sakura ranchu, matte ranchu, etc.. these are only those i can think of. goldfish are as varied as dogs—more varied than koi in both body shape and color. we westerners have seen only a fraction of a percent of what is out there.
goldfish have very complex genetics and there is always much variation in any spawn. an example, young tosakin will often throw nymphs. nymphs are not really a breed but rather a single tailed version of any short body fancy goldfish. the same tosakins with throw relatively few nymphs later as they mature. however a toma saba is a short bodied fish similar to a ryukin with a single tail and is a breed. the difference is that a nymph can potentially throw offspring that reflect back to the appearance of the original breed where as the toma saba should throw toma saba only—fantail nymph can have offspring that are fantails but a toma saba should not have anything but toma saba. there is porbably a whole debate that can be had from this paragraph alone. this is a symplified explanation of a complex genetic topic.
goldfish can be broken into types. "wild" which are longer bodied fast swimming, fancy which have double tails and short bodies, and egg which lack dorsal fins. there are grey areas between them such as the wakin which has a long body but a double tail. eye, fins, color, scales types are added features of clasification the the 3 main body types. the closer a fish body is to the wild type, generally the hardier it is. a major error in the original post has wakin as a tender fish when it is among the most hardy of goldfish breeds and can be kept with the most aggressive and large koi in the coldest of water. all breedes are all the same species and have very similar tollerences for temperature. one should narrow the spectrum by a few degrees from the wild types for the fancier types and you are in safe territory for the fancier types. 68F is the ideal. a good rule of thumb is if you are comfortable, so are they. a tropical 78F is TOO hot and will reduce the fishes' life span to about 5-6 years—you can't keep a apple tree alive for long in a greenhouse without winter and the same is true for goldfish, they need a hybernation or at least a cool period to maximize their lifespan and health. if you keep the fish indoors and out of the sun with no heater, your temperatures are likely perfect. if you keep your fish in a pond outdoors, summer heat is more an issue than cold (hot water has less oxygen and goldfish like trout have poorer gill function in this regard than do tropical species of fish. as long as there is a hole in the ice for gas exchange the fish should be fine. you should NEVER feed below 50F and only low protein food below 60F. fish that die in the winter usually die from food rotting in their gut, not cold. I keep tosakin (repudiated as a very weak and delicate fish) outdoors year round in zone 5-6. I lose more fish indoors in the winter than out. it is more about water quality than temperature with goldfish (within reason).
When selecting a breed, the container and the contents thereof are the true factors to consider, not temperature. tosakins need calm water, bubble eyes need to be kept from sharp objects, slow moving fish compete poorly with faster fish, telescope eyes have a hard time seeing floating food, celestials can't see sinking food, etc. short of allowances for the body type, there really is little difference in environmental tollernaces.
koi are crucian carp and goldfish are gibel carp. they are not the same breed. they can hybridize like a horse and and ###### do to make a mule, but they are not the same species. koi/goldfish hybrids are generally sterile green koilike fish that ironically are more cold hardy than both parents. koi have barbels and downward facing mouths as bottom feeders and though they have many color, scales and fin variatiosn on have a single body type. goldfish lack barbels and have forward facing mouths as intermediate feeders. koi are slightly more cold hardy, but otherwise similar in most aspects.
it pleases me to see beginners taking interest in goldfish to this degree (no pun intended). just be careful of the source of information. forums are generally as good as they are poor sources of info. check your facts with other sites or books. if there are discrepancies, somebody must be wrong (there are errors on wikipedia and bristol aquarist in my opinion. unfortunately the true experts don't speak english and those that do don't care to correct the follies of us amatures). i hope i did not offend anyone as that was not my intent. discussion and even arguing if done civilly is good as it brings out experience and information to others and gets us all closer to the truth. my only intent is to correct some errors before they spread and made a simple and fun pastime seem overly complex. Kudos to the original poster for taking the time to compile the best info he could find—it is not easy unless you can read chinese and japanese.
just keep the water clean and take out the heater and you will have happy long-lived gold fish no matter the breed.