You will find them! They are out there, somewhere, even though you don't know where yet. Take your time and get the right horses for you, because once you have them they (should) be with you for a long time. Getting a horse or horses that aren't the right fit for you is going to cause a lot of heartache and frustration.
I have a friend, who, like you, is just getting started with horses and she is super excited. She leased a full sized horse for a while, but realized that riding isn't so much her thing. She decided that she wanted a mini for driving and just being a fun pet. Though she was really wanting to get started as soon as possible, it took a while to figure out exactly what would work best for her, and then finding the right one. At first she was thinking about young horses so she could have it for many years before it died, but then I helped her to understand what it really means to train a young horse. This isn't generally a good project for a beginner. Then we looked at rescues and while this seemed like a noble thing to do, again, it wasn't the best fit for her, because she really needs a horse that doesn't already have "issues". Eventually she fell in love with a wonderful older gelding. He's 18, but healthy and should have many more good years. He's been cared for and handled well for his whole life, and is an experienced driving horse who's "been there, done that" who can help her to learn. He is well behaved and is completely safe. She is adopting him for free because a great forever home is what his owner is looking for. If she had taken the first horse that she looked at, she wouldn't have found him.
I just say that to encourage you to take your time. It will be worth it when you find the right horses.