Tangs for the most part can be considered reef compatible but there are some bad apples out here that have been reported to nip at corals. As long as you first meet the tank size requirements for the tangs you want, you should be fine in that aspect.
Large angels on the other hand will nip at a wide variety of corals. There might be a few options however, corals such as gsp, blue star polyps, and xenia may be able to out-grow any damage the angel may cause, but that's not a guarantee. I've seen a Queen Angelfish firsthand eat zoas, mushrooms, LPS, and SPS corals as if they were placed in the tank for it to eat.
Angels of the genus
Genicanthus may be a better option than the typical "large angelfish" species we normally think of for a reef tank. With them you're looking at fish like the Bellus Angelfish, Lamarck's Angelfish, and Spotbreast Angelfish. Most are considered somewhat "reef safe" but I generally try to avoid that term. Some of those fish are pretty seasonal and hard to find sometimes though.
If you really want a large angel, FOWLR would be the most financially sound decision IMO, you could have one of those and a reef tank on the opposite wall in the same room

otherwise you may face a lot of heartache seeing a beautiful fish steadily eat a lot of beautiful corals.
Good luck with the planning process! I'm currently doing the same for my future big reef tank!