I agree, a quiet personality is my favorite when it comes to riders or horse people in general. Loud, pushy, or bossy people don't do well with a lot of horses, or have too much to prove. That doesn't mean you can't be assertive.
Anyway, do take your time. Go slow, very slow. Avoid being blinded by the idea of getting a horse. The last thing you want is to get a first horse that takes the fun right out of it. Don't close your eyes to red flags. In fact, look for them. I've bought three horses in the last four years, and got two out of three right, but the one of them was, and still is, a bit of a train wreck. We still have her, and are still trying to fix her issues because I can't, in good conscience, rehome her right now. I wish I had paid attention to the red flags. Also, require a trial. Do not take on a horse without a trial of some sort. She's the only one for which the seller refused to do any kind of a trial. For our first horse, we had a 10-day buy-back contract which allowed us to return him within 10 days if he didn't work out, and for our third horse, we had a 6 month trial because he came from a good friend who trusted me and figured it was one less horse for her to feed over the winter (though that kind of arrangement is highly unusual - maybe ask for a two-week trial or buy-back period, and get it in writing). I don't think it's a coincidence that my two other horses, who are awesome, did come with a trial. The owners had nothing to hide. On the other hand, I believe my problem mare was drugged when we rode her. But there were little things I should have paid attention to... learn from my mistake! Insist on a trial!
You want to have fun with your horse (great goals, btw) so you should probably get a horse that is pretty chill in temperament and is a good, all-around horse citizen. Personality may be more important than high-level training in your case. You want a horse that is willing and happy to move forward, but not the type of horse that gets worried about everything, or refuses to work in certain conditions. In other words, avoid really high-strung, jumpy horses. Trails can be scary places. You never know what you will run into. That nice relaxing trail ride can quickly end in disaster on the wrong horse. So when trying this horse, take him out on a trail. Preferably with another horse, then by himself (even if it's just a short loop alone to see if he is ok being separated). Make sure you have a good whoa, that you can steer, and leg yield (important things on a trail). And because you also want to do a bit of jumping, work the horse in an arena (indoor our out) as well. Go ride the potential horse twice. I used to go see the horse by myself first, and if I thought it had potential, I'd bring my coach on the second visit (I didn't do this for my problem mare). She'd often ride the horse too. Then, if all looked good, I'd get a PPE.
In terms of age, while it's true that an 18 year old can be a very solid horse, you have to keep in mind that you will have a limited number of years left to ride a horse that age. But they can be amazing, and if you're ok with just doing light riding, then you can definitely pick up a really great schoolmaster horse at a good price. Younger horses are usually a bad idea, but my third horse was only 6, and only had about 10 rides on him. I never thought I'd buy a horse that young, but he's wonderful. We're bringing him along in terms of training, and to my amazement, he is progressing very well. So while I don't recommend this for most people, there are exceptions.
Finally, I'm all over the place in terms of breed. I thought I wanted a quiet QH, but the first horse I bought for my 10 year old daughter was a fiery Arabian. And guess what, he's the most solid citizen of all three. We can take him anywhere, he is a perfect gentleman, a very safe mount for my daughter (now 14), and has won two division championships in Intro Hunter classes, not to mention dozens of firsts in all kinds of flat classes. However, he's not crazy about trails. He will do them, but it's not his favorite thing. My new guy, who has now just turned 7, is an Appy. I was never really attracted to this breed, but have fallen head over heels for this guy. Appies can be jumped, but they also do really well on trails, being quite rugged and bold horses for the most part because of their Indian pony ancestors. My Appy loves trails, and is the first horse I ever met who does NOT want to go back to the barn when we finish a trail! He is also funny, interesting, curious, loving - a great backyard horse.
My problem mare? A QH. Spooky, anxious, moody, unpredictable... not that this is representative of the breed of course, but each horse is an individual. Breed stereotypes are just that. Focus on what's available in your area. Find horses you can ride a couple of times, and whose owners will be willing to do a trial. Try out a lot of horses. You have time, so take advantage of that. And good luck finding your dream horse!