OK 75 gallons....
Sharks.. definately no.

My 220 gallons isnt even large enough to give a shark enough swimming room.
Puffers... Not reef safe and most grow huge.. far too large for 75 gallons. Also very aggressive and only fish capable of taking care of themselves should be kept with them. Definatley not Lionfish as they will be harrassed and killed by the puffer.
Tangs... Almost all need 100 gallons minimum.. although perhaps you could get away with a Yellow eyebristletooth as they do seem to be happy insmaller tanks.
Mandarin.. risky.. need LOADS of liverockand mature liverock. The tank needs to be running for roughly 12 months before a mandarin is housed and i recomend a minimum of 100 gallons ow tank to be able to keep the amount of live rock needed to sustain a mandarin. If howver you can find a manadinr that feds on frozen food then your tank size is fine.
Fish Like mandarin? Basically the same advice as above.. although a scooty blenny does seem easier to ween over to frozen foods. remember if you add similar fish to a mandarin these fish compete for food and thus the amount of live rock needs to be even larger.
Delicate Beauties? Err not sure what you mean... nearly all marine fish are delicate and beautiful.
Larger saltwater fish need larger tanks sizes than you are going to get im afraid. Possiblt with eh exception of a lionfish or moray but they give out so much waste that not many other fish can be kept with them.
Snappers etc.. too large for your tank.
Butterflies are ok but need careful aclimatisation and good water quality. Not reef safe as they eat corals (perhaps a copperband is ok but they are hard to keep) Good fish for a fish only system
Angels... Very large family and not easy to anser.. they range from pygmy angels, dwarf angels and large angels. Most are 50/50 when it comes to being reef safe although people get more success with the smaller angels in a reef than larger ones. Large angels wont take to 75 gallons very well when fully grown so i recomend dwarf or pygmy angels.
From the list you seem to like the large aggressive looking fish, this is fie of course but 75 gallons is far too small for many of the fish you seem interested in. Im taking a guess here when you say 75 gallons but is this 75 US gallons or UK? if its US gallons thenthe tank is even smaller and really should not house the larger fishyou have listed.
