There are plenty of breeds you could be considering here. Not all thoroughbreds are as hot and powerful as what you describe in your current horse, so even the right thoroughbred or thoroughbred cross might be ideal for you.
You need to make a list of what criteria you're looking for. How tall do you want the horse to be? What age range are you looking for? What kind of experience do you want the horse to have? Where do you really want to end up? etc. Then go from there.
With your current troubles and your want for something that you can just get on and enjoy, I would not recommend a horse that is too green. Look at horses that are older than 5, with some trail miles, some experience showing, and some solid gaits on the flat. The horse doesn't need to be perfect, but should at least be level-headed and rideable. If big is not your cup of tea, then look for horses between 15 and 16 hands. Reject anything with a history of lameness or injury, or anything with major conformational faults. If you stick to this, you should be able to find a horse that is not scary, but also has the potential to be competitive and let you learn and advance. If you want to pursue dressage over any other discipline, then look for a horse with a start in dressage or at least one that shows potential. Your trainer should be able to help you identify a horse with potential.
I went through the same thing you are going through. About 3 years ago, I was living an extremely busy lifestyle. I was about to graduate college, was engaged, applying for jobs, about to move out on my own etc. I had a green appaloosa filly that was my project starting in High School. She was great project for me then, when I had the time to work with her, but as time went on she became progressively more moody and aggressive. She was high energy, and mean. I kept putting her in training, and her behavior was not improving for me, and I knew it wouldn't improve if I didn't get my act together and figure her out myself. I needed to spend more time with her and really work to put her aggressive energy to good use. Sadly, I was just not in the position to do this, and I was getting nowhere. Riding wasn't fun anymore and I was starting to fear her.
I really just wanted a good horse that I could ride without fearing for my life, that I could work with, but at my own pace. I ended up with a Shire/Thoroughbred cross. This horse was much bigger than the horse I had just sold, but her personality is so much sweeter. She's not nearly as high strung. I can take her on trail rides and to shows and she's not a freak about it. I don't have to lunge her to get the edge off before every ride. I don't have to deal with the tense, aggressive, rearing, bucking mess that made riding no fun. And if I don't ride for two weeks, she's the same horse the next time I get back on. I can just relax, and ride, but she's was also somewhat green with lots of potential, so I still have plenty to work towards and lots to learn with her. A draft cross was not in my original plans, but I'm glad I kept an open mind because I am super happy with my choice.
Basically, you need to be looking at each individual horse's personality, more so than breed. Definitely look into Arabs or Anglo-Arabs if that's what you like. Paints and Appaloosas are promising breeds, as well as Thoroughbreds, Quarter Horses and Appendix Quarter Horses. And don't underestimate the power of a nice, English-type grade horse.
Good luck in your quest to find a new horse. I hope everything works out for you and the horse you're selling!