Addressing the main question.
The invasion of Sicily was am must.
Attack on Italy should be better prepared - especially with the netire later struggle for Cassino in mind, which later was wasted too -thanks to stupidity of Clark of course.
When it comes to the next step. I think tah landing in Yugoslavia/Albania was the best possible scenario.
From 1943 Hungary and Romania (Bulgaria too) tried to negotiate their way out of the entire war.
The events of 1944 clearly show how fragile was German situation in the entire region.
Besides only this could deprive Stalin of his later conquests.
Invasion of France gave the allies certain support from the newly organised French forces, but attacking the Balcans would attract immediate support of much larger forces and might activate Turkey as well.
French forces could be used in Italy this way or in some sort of supplementary attack on southern France (this would support attack in Italy as well).

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