I agree with Sopheria, mostly. I'm not sure he could go higher than 4th, and 4th may be a struggle for him. I'm not a professional though. This is just my opinion.
I think you could do quite well with this horse. He's good for what you say you need. I've taken Arabs to 3rd level and we've won at USDF rated shows against pro's. If the training is solid, he's got 3 good gaits, and he's sound, then nothing is stopping you from being successful with him to the level you want to go.
Correct me if I'm wrong, but you look like you're in your teens. Pretty soon you'll have college and poor paying jobs that will get in the way of your riding. Not that it meanns you can't achieve your goals, but you need to factor all of your goals into planning your future with this horse. It will take you at least 3 years to achieve third level. What will your finances be at that point? What time constraints will you have? It's good to have goals, but realistically, you may may only have enough time to hit third before you're swamped with college and work. Purchasing a horse like the one you posted about will give you the opportunity to move up, yet still allow you to recoup your initial invest if you need to sell him in a few years to pay for college. All I'm saying is I think this horse suits where you are currently, and where you may be in 3-4 years. As long as he vet checks okay, I would buy him.
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