Questions about planning trip to Italy

Just like your other thread about travel in France, your starting point should be a good guidebook. Rick's books are very good at answering many of your questions. As are the various other sections of this website, most especially the travel tips section.

Your questions are pretty open ended. I'll try to answer a few.

Q1 - Off season from mid-November to maybe late March would be the cheapest and least crowded. On our last trip to Italy, we went early/mid December, leaving the Sunday before Christmas the next Saturday. There were practically no lines anywhere. We had "The Birth of Venus" in the Uffizi pretty much to ourselves. The Tuscan countryside was a joy. We were the only guests at our agriturismo. We also enjoyed off season rates. A week's stay in our Tuscan agriturismo was less than $500.

Q2 - Gosh Italy is big and varied. Everyone mentions the trinity - Rome - Florence - Venice and it's hard to argue against visiting them. However, there's so much more to see. I think if you visit cities alone, you miss a lot of the character of Italy. You need to divide your time between cities and the countryside.

Q3 - How many people? How long? what kind of accommodations do you like? We spent 10 days on our trip. Not counting airfare, we spent ~$3,000. That includes all meals, lodging and transportation, which was a rental car. Our agriturismo was lovely but not luxurious. We actually prefer to stay at smaller B&Bs that are modest. In addition to being less expensive, they are more fun!

Q4 - Eat a big breakfast! Snack at lunch. We often bought cheese, bread and fruit at the supermarket to eat at lunch. We sought out small family restaurants. We ate a fancy dinner twice.

Q5 - We try to book about 4 months in advance.

I understand not all countries or cultures are used to using book travel guides. They are very useful and I noticed that several are offered on Amazon. If Rick Steves isn't readily available, you could see if Lonely Planet is available to you. They offer 'On a Shoestring' guides for continents and some countries. It might benefit you to try and source 'Europe on a ShoeString' for strategies of how to travel on a budget within specific countries.
From Canada, I book air fare at least 6 months prior to travel often 8--10 months prior. This is my mental switch that I am committed to this trip. As I use short let apartments which often include deposits, I don't book them until flights are booked. I book apartments 6-8 months prior as I am also a budget traveler, so know I can lock in costs with the features I want. I save money on food by using apartments, and they are often cheaper than hotels.
I pay whatever is needed for museums, sites and activities. These are the reasons I travel. I rarely buy 'skip the line' tickets because I travel off season. I make up my savings by cooking in or picnics. Because I eat breakfast in, I have a big lunch, often from the 'menu of the day', and more cold spread for dinner.
I walk or use local transport in the cities, so it is just the train costs between cities. These can be purchased when they come available (not sure for Italy - maybe 60 days?).
Typical starter cities are - Rome, Florence, Venice. It could be done in 9-10 days
For flights, unless a return flight saves hundreds of dollars, it may be more cost effective to fly into one town and out another town. It is certainly more time effective.

Q2: Which places/cities do you recommend for first time visitors to Italy?

Many people will tell you Rome, Florence and Venice.

I think the true answer to that question is the answer to the question you should pose to yourself : "What is it that is drawing me to Italy (or France, or Tahiti or China or Australia... WHEREver you plan to visit)?"
Nobody can answer as well as you can because nobody has the same exact reasons for wanting to travel somewhere.

Likewise, nobody can answer precisely for you "what are the 'must sees"?"
They can answer what they enjoyed and what they would encourage like-minded people to see and do.

Best is to read about Italy (or France, or Tahiti or China or Australia... WHEREver you think you might go some day) and find out what appeals to you. That will tell you where to go. Then you find out what's special about the places you want to see and that could tell you WHEN to go (Sept-Oct for Munich and its famous Oktoberfest, mid-July or early August for the Palio horse race in Siena)

Find out what you'd like to do and the answers to where you should go will follow. Then you ask people which of the (likely) many places you've put on a list should you combine for a sensible itinerary. And then put the rest on hold for the next trip (and the one after that...)