I agree with harlequinduck. There's a lot you need to consider before you buy a horse. Just some things to think about-
What are you going to do with the horse? For hunter, jumper, dressage- thoroughbreds and wamrbloods are great if you're competing in high level competition and can handle a horse with that much energy and that many needs. Generally they are harder to keep weight on because of high metabolisms and also need to be exercised often otherwise they can become anxious, jittery, and dangerous. If you want to do barrels, poles, flags, reigning, etc. Go with a horse that is stockier all the way around. Quarter horses, paints, appaloosas, and mustangs are great for this because they have thick bones that wont splinter/ break under the pressure that these events provide. A thoroughbred on the other hand can do these but are much more likely to suffer leg injuries plus are not built to make sharp turns because of their long bodies. If you want endurance you've already got the breed. Arabians are top of the breeds for this because of their stamina. For endurance you'll want a slim horse with lots of stamina, a good heart, sound hooves, good conformation, and good lungs. For this I personally use a Tennessee Walking horse and a quarter horse X morgan. The QH X Morgan is a little stocky for it though.
If you're looking for just another horse to take out on trails and play with get one that is calm, doesn't need to be ridden often, and is an easy keeper. Such as quarter horses, Tennessee Walkers, Halflingers, morgans, and appaloosas are great for this. (Sorry if i'm a little biased on breeds, I come from the US and mainly do barrel and gaited horses)...
That's another thing to think about in a trail horse, gaited or not. Gaited are smoother to ride at faster speeds and naturally walk faster. Non gaited you'll have to post every time you go fast but they are great for leisurely walks and enjoying scenery. Gaited horses can include (but not limited to) Saddlebreds, Tennessee Walkers, Paso Finos, Missouri Fox Trotters, Morgans, some mules, Icelandics, Rocky Mountain Horses, and National Show horses. Not gaited are ones you have to post on like paints, QH, thoroughbred, warmblood, etc.
Riding experience is also important. While rescuing a horse can be a great experience some have serious issues that take very experienced riders and have special needs in riding. If you've never trained a horse or have someone who can help you work out the kinks I wouldn't suggest adoption. Most adoption cases involve starvation and abuse. This can make them very possessive, have certain fears (such as one of mine is an adoption but she used to be afraid of men in black cowboy hats. Tan, white, blue were all ok, even it being black on a woman was ok. But get a black hat on a man and she would flip out), and can come with underlying medical problems (which can get expensive). You need to be realistic in your riding experience and look for a horse that has something to teach you without blowing you out of the water. If that makes sense.
Also consider where the horse stands in its current herd. You have two babies and a pony, an aggressive dominant horse can do serious damage to them. I used to have a mare who was fine with geldings but would quite literally fight to the death with other mares, and a gelding that was fine with horses but wouldn't stop harassing my pony and babies (he quite literally almost ran them to death one day... I have since gotten rid of him).
Age and training you also need to consider. Four and under tend to have not completely finished their training and can still be a little skittish. Also new born- 6 years haven't completely stopped growing and fusing their bones yet so you couldn't ride them as hard as you would a normal horse without risking some of their soundness (also depends on breed QH are fully developed by 4-5 because they have stockier bone structure). 7-15 years is generally the prime of most horses lives (though if taken care of very well it can last into the late 20s) 15+ years horses are generally much calmer (especially if their ridden often) and have most the spark and kick out, though not all. My pony is 38 years and he still runs, bucks, and chases our dogs...
As for gender it's really preference. If you like spark with lots of heart but can be moody and temperamental go with a mare. If you want one that's pretty laid back but lazy go with a gelding. Stallions can be sweet but you always have to separate them when a mares in heat and on trail you have to watch out for mares. Plus they tend to be more aggressive, dominant, and difficult to handle because of the testosterone. These are generalizations of course, but they prove true for most.
Also think about your parents. When you leave the home for good/ college who's going to take care of the horses? Are you going to take them with you, let them go into hiatus, or sell them. Older horses can be harder to sell, while younger horses in hiatus can fall out of training, taking the horse with you can be expensive too. I'm going off to college next year but am taking my 3 yr old with me. My friend had wanted to get a horse also, but her parents didn't want to have to take care of it after she was gone. Just a random thing to think about.
Finally never settle. If the horse isn't what you're looking/ equipped to handle don't get it. I've seen to many good people run over by bad horses that they thought they could fix, or good horses turned bad because they rider couldn't handle them. Also some horses can be great but just don't fit your personality. If you do get that type of horse it'll be great at first but in the long run you'll probably be miserable. There's a horse out there for everyone, take your time to find him/her.
Oh if you need buying tips I've got those also, but this post is long enough so I'll leave you with that. Hope this helps- Whisp