Suggestions for websites with the best flight options?

I use https://matrix.itasoftware.com/

You can put in a calendar month and a range of a number of days you want to be there and get a calendar of lowest prices. Some you might not care for like Turkish (nothing wrong with them, just requires a flight to Instanbul and back tracking), but you can filter those out. You can try different airports and find low priced flights. They only tell you the itinerary and price. You still have to buy tickets direct from the airline.

Kayak gives you the option of nearby airports and arrival and departure dates plus or minus three days. But you’d best start thinking where you want to go and what you want to see (Italy is big and diverse) as well as a rough idea of travel dates or you will drive yourself nuts. Beware of bargains that involve multiple plane changes and/or very long layovers. Another good tool is Google Flights. But, when you finally decide be sure you are booking with an airline and all your flights are on one ticket.

Google flight matrix. Pick flights into any city, any dates. Gives prices, but buy from airline.
Make sure while checking for layover times if applicable.

Start looking now, you're going to need a reference point. Set alerts and buy when you see a great deal.

I usually start with expedia to get ideas of flight routes/times/prices.

This site can be useful for determining where you can fly direct to/from
https://www.flightsfrom.com

I also use skyscanner.com to monitor price changes

But I always purchase tickets directly from the airlines, for many reasons.

I'm another Kayak user; I find the site easy to navigate and I feel pretty confident it is showing me an accurate range of the flights & prices available.

However, once you choose the flights you want, make sure you are on the actual airline's website to make your purchase. If you are on a third-party website it can be a hassle to contact the airline if you need something like a request for an in-flight meal. Kayak can direct you to a third-party site without your realizing it, if you don't look carefully.

I start by looking at Wikipedia and seeing what airports within driving distance have non-stop flights where I want to go. What I'm looking for are the budget European airlines like Norwegian Air Shuttle that cost 1/2 the airfare of the big "legacy" airlines.

I otherwise use MatrixITAsoftware and Googleflights to figure out the cheapest airfares otherwise. They have calendars that show a whole month of airfares, and prices do vary daily.
If you'd have said what your departing city is, we could easily tell you what your best value is. Getting into Italy is generally more expensive than many other airports in Europe. Rome FCO is the largest airport with Milan second most popular. But flying into Milan is a long way from the most popular travel cities of Rome, Florence and Venice. Many flying into Italy from other European cities fly into Pisa--one hour west of Florence--and take the 1 hour train ride over.

I use Google flights too. Prices change constantly so put a request in for alerts for your locations, dates.

rachel,

One method you could try is to use a website like Expedia or https://www.hipmunk.com/ to get some idea of routes and prices. Once you've got some idea of available flights, check them on the website of the airline you've chosen.

I normally use the internet to research flights, but always book long haul flights with a travel agent.

Keep in mind that airlines in the US do NOT allow anyone to discount their published airfares, so whatever flight/itinerary/price you find on any online travel agency/airfare aggregator site will be exactly the same as what you will find on the airline's website. If you happen to find the exact flight cheaper, I would be extremely cautious

Otherwise the usual suspects - Kayak, Google Flight and Hopper would be good places to start......

kiwi.com will give you the cheapest flights, bar none.
with a huge caution:
They do not use codeshare airlines. So you must choose wisely regarding layover timing. You will get the absolute cheapest combinations this way, but it is best to do if you plan on CARRYON ONLY. Not recommended if you plan to check your luggage, as that introduces too many variables. Also, for their prices, you cannot choose your seats.

We recently used them for US to Spain, Spain to Italy, Italy to US (all different airports). $1500 for two. One of the connections was ridiculously close (1 hour 15 mins returning home through Boston) but we knew that going in, and were prepared to stay overnight if necessary (we made the flight). We also ended up sitting together on every flight.

Good luck!

Define "best".

Are you simply looking for the cheapest possible ticket, to the exclusion of every other consideration? That's often what people define as "best" but that often results in a really awful experience. Be careful that you know what you are buying.