Are you sure your tank is cycled? (I suspect it probably is, and is fine.) Did you "feed" the tank, so nitrogen fixing bacteria would grow? Have you monitored changes in ammonia, nitrite, nitrate? I asked about the live rock, because several years ago I ordered live rock that came in dead (in the box, it had maggot casings attached). I thought it might still have some "live" bacteria on it, but it took me many months to get the tank cycled. Seemed like forever.
Even if your tank is cycled, add fish gradually. Keep up with water quality parameters, especially nitrites and ammonia. Be prepared to do large, partial water changes, if necessary. Invest in a QT and have it set up.
Some comments on your fish list: honestly, the trigger, angel and blue tang will pretty quickly outgrow the tank, and I predict aggression problems with that many fish, even when small. I would get fish that can live out their adult lives in a 4 foot tank.
Also, never believe anyone selling fish on what is the appropriate minimum tank size. It's a conflict of interest. Even F&S, my favorite online retailer for fish, gives tank sizes that are too small. I would check tank size information here. A good site to get adult size for many species, as well as other useful information is
www.wetwebmedia.com. I'd check LFS claims for adult size there as well.
I added some ideas for substitutes to your list:
1 Annularis Angelfish
**substitute a dwarf angel - flame or coral beauty are good choices**
1 Saddle Valentini Puffer (Canthigaster valentini) - okay to keep
2 Ocellaris Clownfish - Tank-Bred (Amphiprion ocellaris) - okay to keep
2 damsel black and white stripe
**I would replace or eliminate, these get too aggressive, and eventually, too big. If you must have one or more damsels, some of the blue damsels are less aggressive. You can also look into chromis**
1 Humu Picasso Triggerfish (Rhinecanthus aculeatus)
**none of the triggers are small enough for this tank, especially with tankmates - perhaps replace with some active, bright colored, smaller fishes like orchid dottyback, six line wrasse**
1 Blue Tang (Paracanthurus hepatus)
**pretty much any tang but a yellow tang is going to get too large for this tank. I'd consider a different fish. Royal gramma is a great, hardy, inexpensive fish with some nice yellow on it.**
If what you ultimately want is a tank that included a larger angel, tang, and smaller (12") trigger such as the picasso, I'd get at least a 125, more like a 180 or 210. The 75 can be good experience before you get a bigger tank.
A great book for selecting fish is "New Marine Aquarium" by Mike Paletta. He has a great list of hardy fish, as well as fish to avoid. Lots of useful tips for setting up, aquascaping, maintaining and troubleshooting your tank, too. This is a great beginner book, to get you the base of knowledge you need to get the most out of the online forums. You can get it for less than $20 on Amazon.
New Marine Aquarium link