I've never owned one of the fish on your list, but I can say for certain that triggers cannot be kept in reef systems. Non-dwarf angels are almost always a no-go as well.
Triggers in the wild eat live coral and poop out the stony skeletons. This is where the highest quality reef sand comes from, triggerpoop. They have hard beaks for this exact reason. Even if you offer it prepared foods, it will ALWAYS revert to eating your corals, no matter what you feed it. I have never heard of someone getting them to prefer prepared foods over live coral.
Angels will not attack coral like triggers will, but they love to graze on live coral. They are hit and miss, but this depends on the individual fish, and not the species. You can try one, but it will probably eat coral. Some people have had success with these, but the key is finding a specimen that prefers to eat prepared foods, and then keeping WELL fed, usually at least twice a day.
I don't have much info on the blue-spot puffer or the marine betta, but puffers are not generally considered reef-safe because they love to eat inverts. Bettas will leave corals alone but are dangerous with smaller fish and inverts. My info about these are very limited.
You could try an angel, and if you can find one that will behave, you'll have success. Sorry for the lengthy post, but I hope it helps. Good luck!
