Welcome to the "Wonderful World of Shermans" Marian.
In order to do an M4A1 for the Italy and North Africa, I'm afraid the Italeri offering won't make it. It is the late version of the M4A1 with large hatches and as you have already noted the late style 76mm turret. Taking a 75mm turret and dropping it on the hull creates a whole different series of problems as in the large hatch hull with 75mm gun has so far been only verified in D.D. configuration.
Probably the easiest way to create an early M4A1 would be to purchase a cast hull from Tank Workshop or Formations and use the Tamiya M4 as the donor kit. You'd also need an earlier version suspension set.
Formations does have a complete conversion available and are highly recommended.
DML did have a kit like this but it is OOP and sells for obscene prices on E-Bay.
Yes, the early M4A1s did have the 3 piece bolted transmission.
As far as interiors, you can use the Tank Workshop or Verlinden M4 interiors with some minor adjusting.
Reference books ..... for any one starting in Shermans and wanting to keep it simple and inexpensive I would suggest 2 Squadron offerings:
M4 Sherman in Action by Bruce Culver
M4 Sherman Walk Around by Jim Mesko
Both books cover the Sherman and it's history quite well for a low cost.
Have fun and don't be afraid to shout when you need help.
Happy Modelling and God Bless
Robert