Stocking a 125 Gallon FOWLR

I recently acquired a complete 125 gallon saltwater setup off Craigslist for $300.
This is what came with it for filtration:
-Two wet/dry filters
-AquaC Urchin Protein Skimmer

I was wondering if what I had in mind for stocking was too much or if the fish were compatible. The setup came with a 6” Blue Tang, a 5” Big Eye Black Bar Soldierfish, and a 4” Blue Jaw Trigger.

This is what I would like to eventually add:
-Yellow Tang
-Saddleback Butterflyfish
-Blue Spotted Puffer
-Harlequin Tusk
-Flame Angel
-Snowflake Moray Eel

I would also like to know the order I should add the fish I am planning on keeping.

Thanks,
Ryan