Case closed.
xeano321 has provided an almost perfect answer. In fact, it is nearly identical to the solution I wrote. The only thing (it’s a tiny thing, so I’ll overlook it) is that you didn’t guess the Two Clues. The point was for you to guess the Two Clues, then wait for conformation. Instead, you wrote four clues and a near flawless record of the event.
However, you missed one very important clue! How do you know he was assassinated and not just murdered by a burglar?
Here is the official solution, with all of the clues (including a few tiny ones you guys missed, which means I'm way, way cooler than everyone. hah).
The two clues were the note and the gun.
The note proved that it was not suicide. The man was a poor immigrant from Italy. He had no family and no friends in the US, and still had nothing on him but European money. There was a magazine in the room, but it was printed in Italian. The only other books he had access to were a few novels and a Bible, but they had “never been opened”. The note was written in perfect English.
The gun proved that it was assassination. Had he been simply murdered, his watch and money would have been stolen. Plus, the gun was presumed stolen, but “the only fingerprints on it were his”. Not only that, but it was “well-polished”. It’s unlikely a man would stop to clean the exterior of a gun before shooting himself with it. The S&W in particular, when polished, retains oil perfectly. Fingerprints stick to the surface easily, and they would have been extremely easy to see. But Angel only spotted prints on the pistol’s grip and trigger. Being a revolver, there should have been a clean thumbprint on the cocking hammer. The gun was too clean.
From the missing, and present, evidence, Angel deduced that a hitman had been contacted by the Italian Mafia to kill Giovanni. An informant leaving the country could have had information that they didn’t want leaked. The assassin was wearing gloves. He entered the room, shot Giovanni, and then wrapped the dead man’s hand around the gun so his fingerprints were planted. Knowing that he didn’t have much time, the assassin grabbed a sheet of paper and a pen from the desk and jotted down a suicide note, leaving it under Giovanni’s other hand and the pen on the desk. Angel narrowed the field even more by realizing the assassin was from America and not Italy. An Italian assassin would have known that Giovanni did not know English.