My advice for beginners is long, but bear with me. I have ridden pretty consistently for over thirty years and have seen beginner mistakes over and over. Take a few minutes and consider some of my ideas as well as those of the other experienced posters.
You will likely get interested in a discipline of riding, such as trails, barrels cutting etc. That is fine and dandy, but before you get too involved doing your discipline of choice, take a couple of *years* and really focus on learning to ride well. Proper, classic, equitation, and also proper handling of horses, especially when things do not go as planned. To do this, find a good trainer and take lessons as often as you can. I think a dressage type trainer would be ideal for starting out, personally.
Before you really focus on a discipline, you should be able to ride easily at all gaits with proper seat and leg position, and be able to ask for those gaits correctly. You should be able to make upward and downward gait transitions, as well as rate your speed within those gaits. You should be able to do a one rein stop at all gaits. You should know your diagonals, leads, and have light gentle hands. You should ideally spend a good deal of time at first on a longe line, simply getting your seat at all gaits (what is known as an *independant* seat) so you will never have a tendency to balance on a horse's mouth, something I constantly see beginners doing.
Additionally you should start to be able to respond instinctively to handle unplanned behaviors. You should be able to know what to do if a horse spooks, bolts, rears, bucks, and you should start being able to read a horse's behavior to notice that those things might occur and corrective action can be taken *before*things get dangerous. The real key to safety with horses is prevention.
Are you starting to see why I emphasized *years*?
That is how long it will take most people to become minimally proficient at all the skills listed above.
These first years of riding, or returning to riding aren't supposed to be a punishment, they are supposed to be fun. You will hopefully get with a great instructor, ride a variety of horses, and start getting interested in one of those disciplines, if you don't already have one in mind. Most of us do more than one discipline, especially throughout our lifetimes. I rode hunter/jumper as a child, did gymkhanas, also rode trails. Now I ride trails mostly, but enjoy working on western pleasure and reining type stuff with my western horse.
In addition to taking lessons to get proficient, *read*. Read as much as you can get your hands on. Watch the clinitions, but don't get hung up on just one and make him/her your guru. The best horse people I know keep open minds and learn from a variety of people and sources, then they use what works best for them and their horse.
After you take a couple of years to get proficient at basic riding, talk to your trainer about the next best step. A lease is often a good option for a first horse experience. Remember that your first horse leased or owned should be bomb proof and possibly older. You may need to move up to a more advanced horse in another year or so and depending on the first horse, and the situation, so keep that in mind. For sure do not make your first horse young (less than five IME), untrained, highly reactive, or a problematic horse with "issues". You need to use your head, not your heart when making the first horse selection, leasing or buying. Listen to your trainer.
All of the above will help you get a good start. Adult beginning or returning riders especially, think about this: if you had a child interested in horseback riding, you would start them (hopefully) with lessons to get a good safe foundation to start, and then a safe gentle horse. Why adults often do not offer themselves that logical start is a mystery to me. Instead, I often encounter adults, who should know better, take a lesson or two, and then they rescue a 3 year old, essentially unhandled, highly reactive, high energy horse. Then they either end up afriad, injured, both and then may end up with even more unsuitable horses for some reason, while keeping the original because they fell in love with it. They simply keep accumulating unsuitable horses. An example of more money than sense in some instances.
Lastly, if you do end up with a horse that is not right for you, for whatever reason, there is no shame in rehoming it. Even the best of trainers don't "click"sometimes with certian horses, and it happens even more often to us amateurs. I bought an unsuitable mare once. I gave it six months of trainers, lessons, then found her another home. You can't win 'em all. It is just as easy (easier IMO) to fall in love with a suitable horse as it is one that is not suitable. Besides...horses can kill you. A horse that is really unsuitable could cost you your life. Our sport is dangerous. Having a good horse and rider match helps decrease that danger significantly.
Good luck and welcome to horses! There is nothing better!!!