No matter whom you ask in the horse industry, picking out your first horse to buy is a very important and involved process. Just because you haven't owned a horse before doesn't mean you can't do it, and just because you weren't raised around horses doesn't mean you can't do it!
First of all, you need to decide what you are buying your horse for. Different temperaments and breeds are good for different activities and disciplines. English or Western? If you are riding English, are you taking lessons or showing? If you are riding Western, are you taking lessons, doing trail riding, showing, or rodeoing? These aren't the only options for each discipline, it's just to give you an idea of how many choices there are in the equestrian world!
Once you have chosen your discipline and activity, you have to analyze your riding and horse-handling skills. I say horse-handling skills because sometimes people are good in the saddle and not good on the ground. If you are a beginner, do not buy a horse that is going to be too experienced for you and too difficult to handle, because that will ruin the whole experience of owning and riding your very own horse! If you are an intermediate rider, buy a horse that matches your level of experience as well, because one too experienced may not be safe or fun, and one that is too beginner and push-button may not be challenging enough to teach you anything. If you have been riding consistently for a long time and feel you are experienced, buy a horse that is appropriate for your difficulty level. Do not buy one that was a school horse for little kids-that just won't be fun-but don't buy one that is too much horse for you.
Say that you have found the horse you want-it fits your experience level, you like its personality, gender, etc.-don't jump to buying the horse right off the bat! Keep your options open. Don't just look at one horse and go "It's the one!" because you might find one that you like better. Make sure you have an open mind towards all horses that you look at. You need to ask a variety of questions about the horse to its current owner. Any question that pops into your head about the horse is a good question, no matter how stupid you think it is. You need to know EVERYTHING. But there are a few questions that you may not know to ask, depending on your experience level. Here are a few that I ask when looking at horses:
Has your horse been vaccinated? Who does the vaccinations? (try and get the vet's information)
Has your horse ever been floated? (had their teeth done)
How does your horse stand for the farrier? Vet?
Is the horse easy to catch?
Does it get along with other horses?
Can it work alone and in a group with no problems?
Is it herd bound? (attached to its friends)
Is it barn sour? (doesn't like to leave the barn)
Is it gate sour? (in the arena, it likes to stay near the gate)
Has it had any major injuries, illnesses, or surgeries?
How does it trailer?
Does it catch, clip, and load?
Is it head shy? (this you will be able to tell on your own, but it never hurts to ask!)
Is it registered?
If not, why isn't it registered?
What experience does it have?
What activities or events has it done previously?
Who has been riding it recently?
There are a lot of other good questions to ask, but read some books and do some thorough research of the horse you like and you'll be good to go.
If that isn't the horse for you, then keep looking! There's a horse out there for everyone. If it is, then congratulations! Now you need to make sure that you have all of the equipment that you need. When you own a horse, it is very important to be prepared for any situation.
The type of tack you get depends on which discipline you ride. If you ride English, you will have to buy an English saddle, bridle, girth, bit, and other accessories that your horse may need. If you ride Western, you will have to buy a Western saddle, bridle, bit, cinch, and other accessories like a breast collar and back cinch if you want to have them.
For other equipment, a blanket for your horse is always handy, as is a cooling sheet. Grooming tools are essential, and anywhere you buy them will be able to recommend to you which ones are best to get and which ones you need. Saddle soap and oil are good to have for cleaning your tack, and a first aid kit is important to have. Again, anywhere you would get things for your horse's first aid kit will be able to tell you what you need.
After all of that, enjoy your new horse! It is a very rewarding experience, especially the first time. But I have to warn you, I didn't follow my own advice when I bought my first horse. I have been riding for almost sixteen years and could never afford one of my own, but I needed one for college so I bought the first horse I fell in love with even though deep down I had some reservations. To make a long story short, she ended up kicking me in the back, rearing, bucking, and trying to roll on me. Please don't make the same mistake I did! It is an expensive and painful mistake, both physically and mentally. Just be careful about the horse you buy and remember to ask questions! I now have a wonderful horse named Moose, who is the poster boy for this site, and he is quite a gentleman. Your horse will be your best friend if you find the right one, so don't give up hope.