I am flying out of the US for the first time to visit Italy.
I'd like to fly into the southern region to visit Catanzaro in Calabria
and fly out of Venice- I'm finding it way too expensive- Should I just fly in and out of Rome and just train back and forth?

It will be cheaper to fly into Milan or Venice and out of Rome. Most people prefer to start with Venice because departure flights from there leave much earlier than Rome.

You might check flights for Venice (or Rome) to closest airport to Catanzaro on one of the budget airlines. Take a look at www.whichbudget.com or www.skyscanner.net.

How are you searching for ticket prices? If you're booking 2 one way tickets that will be expensive regardless of the cities. If you're using the multi-city feature to search for fares you're doing it the right way.

Using www.kayak.com I'm seeing flights from Chicago to Bari or Brindisi, returning Venice to Chicago, mid September, for $750. Flights to Naples, returning from Venice for about $100 less.

Lamezia Terme would be the closest airport. Bari and Brindisi aren't very close.

Using www.kayak.com I'm seeing flights from Chicago to Lamezia Terma, returning Venice to Chicago, mid September, for under $700.

Ditto above. Make sure you are looking at an 'open jaw' on the same ticket, not two separate one-ways. It's not always easy to figure out (multi-city) online. You can call the airlines for additional assistance.

On UA's site it is called a multi-city trip. It's really quite easy to price out.