From a visa perspective, the easiest way to think of the Schengen region is as if it was a single country, with multiple states. That's not technically correct, but it's close enough for most situations.
In your case, you'll arrive in Italy on an "international" flight (from a non-Schengen state), and you'll depart from Italy on a Schengen "domestic" flight (to a Schengen state) - thus you will go through immigration in Italy. Based on that, your first point of entry will indeed to Italy.
Despite the fact you'll go through immigration in Italy, within the Schengen region you go through Customs at your final destination - thus there is no need to collect your bags at your first point of entry as there is for some countries. Thus presuming your airline is able to check your bags all the way through (which in general they will be able to do, presuming it's the one airline and/or booked as a single ticket) then you will NOT need to collect your bags in Italy.
A schengen visa generally allows you to travel to any country in the Schengen region - even if you didn't specify them when applying for the visa. That said, as with any visa application it's never a good idea to lie or leave out information. If you think it's likely you will visit Germany and Austria then you should list them as destinations on the application. If it's more of just a "plans might change and I might go there one day" style plan then you could just as readily leave them off - if your plans do change and you end up there then you won't have any issues as a result.