Fins take time to develop, so a fish with large fins (particularly halfmoons) is usually at least six to eight months old. Young halfmoons (three or so months) look like plakats, but the number of branches in the tail gives them away. Young plakats look like females, so be careful. Fin branches are always even. If you have a look at the number of rays in the tail, wherever you see it branching into three, five or seven it means that another branch is growing and the fin is not developed. This is an indicator of a young fish.
Bends in the spine are unfortunately fairly normal and are caused by the weight of the fins of halfmoon and veiltail bettas. The spine is not built for this much weight and because the huge fins have been bred in with only a few hundred generations the spine has not had time to adapt. The same is often seen in fancy guppies and the older they are the more pronounced the deformity and the fish's discomfort. So unless the bend is severe (more than 30-40 degrees) or skews sideways, or there is an obvious deformity of the spine as opposed to a bend, don't worry. You're going to see it everywhere. A bent spine in a betta with short fins is probably a congenital weakness; fine for a pet, certainly not fine for a breeder.
When you go to choose which betta you'll take home, watch them for a while. Do not buy one that does not move, that rests on the bottom or hangs motionless at the top unless you are prepared to do a lot of work rehabilitating a betta with serious and potentially permanent damage caused by long term exposure to ammonia. Do not buy one with a distended belly or if there are any food pellets on top of the water. Bettas that are healthy are pigs. They will eat until they literally can't eat any more and end up constipated for a week because they ate so much. Uneaten food is a pretty big sign of a sick betta, as is a distended belly which usually indicates constipation.
The betta you want should be moving around as much as the cup permits it to, or should at the very least show interest when you approach the cup or if you swap the cup around so that it's looking at a different potential rival. A betta that will not flare at a rival male or that will not move unless you touch him (as opposed to his cup) is probably not healthy. Contrary to popular belief bettas are not sedentary lumps that hang at the top of their tanks. They do this when they are bored, stressed or have essentially given up and decided that life is not worth the bother. If you are sure that this is caused by loneliness or boredom it usually goes away with a change of environment but if you're inexperienced with bettas it's wisest not to take the risk on a lethargic betta.
Ragged ends of the fins can have several causes. If they aren't bleeding, aren't darkened and generally look healthy the betta may be a combtail. Combtails occur on all fin varieties; they are the variation that was selectively bred and enhanced to create the crowntail. They may be of any length - slight extensions of the rays to half the length of a standard crowntail. Ragged fins can also be caused by fin chewing. It's a nervous habit common in bored and stressed bettas such as those kept in barren pet store cups. Sometimes it goes away when a betta is moved to a stimulating environment with clean water. Sometimes it's habitual and you can't do anything about it. Bettas almost never cause themselves serious harm, they just look awful.
Watch for finrot though, the pet store cups and the ammonia seesawing often cause it. if the tips of the fins are red don't buy. THis could be developing septicaemia which is very hard to cure.
A degree every day or two until you get him up to a decent temperature should be fine. Bettas can be acclimatised to cold water but they don't eat, look miserable and generally fail to thrive, and IMO it's cruel to try and keep them that way. You want a fish for a coldwater desktop aquarium, buy a paradise fish. I don't understand why pet stores do not even try to understand the basics of betta care.
The better conditions they are kept in at the store, the less likely it is your betta will have ammonia damage.
