First of all, what breed are you interested in? No breed is really 'better' than any other, it all has to do with your interests and what you're looking for in a horse. I guess you could say you choose your horse's colour...you can buy a horse of whatever colour you want...the other things can't be chosen so much as bred for. Below 2 years old, horses age by .1 years per turn. After that, it drops to .05 years per turn. Now, the more complicated stuff. After you've chosen a breed to focus on, you'll want to decide what to train the horse in (if it isn't already trained) and what you want to do with your horse (i.e. breed, show, etc.). If you're looking to breed or show, you'll be interested in
stat maxing. A stat maxed horse is one whose Surefoot, Strength, Speed, Endurance, and Intelligence is all over 200 in the parentheses.
An example of a stat maxed horse. Don't get drawn into the whole level thing...a level 15 horse doesn't mean much by itself if it isn't also stat maxed. The number inside the parentheses is what is important for breeding, and has a huge influence on how well horses do in events. By training your horse in the different training options, the number inside the parentheses will rise. Eventuall when the stats combined add up to 450, you'll get a message when you take a turn that says 'This horse has reached a statistic cap'. This is a good thing, but don't stop training here. Now, one thing to keep in mind: It's really really difficult to stat max a horse on a novice account. If you have the extra money, you might consider paying a sponsor to train for you. But it's important to remember that the better trained your horse is, the better the offspring of the horse will be. Really, there's no 'right' or 'wrong' things to do in the game. I know it's overwhelming at first, but you just need to start playing, and you'll get a feel for it. It is possible to find a good yet inexpensive horse, it just takes some searching. Hope my long winded response helped a little, and feel free to message me if you have any more questions. ^_^
