Wow, that's a lot to take in. The Trigger will out grow that tank in short order. They can grow up to a foot in length and need a 180 gallon at the minimum. The Moray Eel will grow to almost the lenght of that 29 gallon when full grown. Those two fish alone will produce a lot of waste as they grow and it will be very difficult to keep the organics down (NO3 & PO4) but most important it will also be a problem to keep the ammonia down if you add anything else as the amount of rock and filtration isn't sufficient to process that bioload. When that happens the ammonia will burn their gills and they will die.
The salinity number you gave isn't right, like Steve said. I keep my tanks at 1.025 specific gravity but up to 1.0264 is ok too. 33.3ppt-35ppt. For the 1st 6-9 months I had my tank up and running I couldn't keep and zoas for some reason. The would close right up, stay closed and melt away. After the 9 month mark they've been fine and I can't kill them now. With coral, you want to wait at least 4 to 5 months before trying to keep them. The tank is just too new to support them. That's not to say it can't be done for someone experienced, but your chances of success will be much better by waiting.
@Mom2Many is very good at keeping smaller tanks and can help you with your stocking options and create a thriving system. Also, have you been visiting any local fish stores beyond Petco? They are usually very good at giving better advice to help get you started, unless you happen to get the right person at a Petco. There are a few but it's rare.