FLights

Yes, you arrange flights yourself for RS tours, and there is no discount.
The general tip is to not use 3rd parties and only book with the airline.
Here's some help on this site:
https://www.ricksteves.com/travel-tips/transportation/booking-flights

Which Italy tour are you doing?

Use Google Flights to find out your options. If the tour starts and ends in the same city, look for round trip flights.

If the tour starts and end in different cities, use the multi-city choice to fill this in.

When you see a flight combination you like, contact the operating airline and book it.

Here's a link to Google Flights: https://www.google.com/travel/flights You will love Italy!!!

With regards to your miles, a lot depends on how many you have. I would pinpoint the flights you want first, and if it is on AA and you can use the miles, then great. But you might get better deals on other airlines, which is why it's good to use Google Flights to see all the options out there.

Feel free to come back here with more questions.

And remember that you don't have to fly to/from the towns/cities where the tour starts and ends. Sometimes it can be cheaper and easier to fly to a nearby major airport and take the train the last bit.

I highly recommend arriving a few days prior, at least, to when the tour starts. That way you can adjust to the timezone and rest up for your tour. It also gives you a buffer in case your flight is late/cancelled.

We generally try to take as many extra days as possible to travel on our own. The rational is always that we've paid the air to get there.

I vote with Jules on going early if you can. It allows you to recover from the long flight AND gives you some flex if there are travel delays.

If you are comfortable telling us which tour we can also give you some ideas on how to fill your time before the tour!

Welcome to the forum and you'll love your first RS tour!

There are companies that will help you maximize your miles, for a fee of course. In case you haven't looked lately, you need a whole lot of miles to get anywhere these days unless there's a special running.

Try signing up for the Thrifty Traveler newsletter, and perhaps Going.

I agree with Jules and Pam, we had a flight cancelation a few years back, and finally arrived in Zurich 24 hours later.
Also, try to find flights that get you over the pond in one connection. Once you're in Europe, so many options exist if something happens to your next flight.
Good luck!

Which tour and when?
Depending on the tour you may need to book flights and plan for train travel to your start and/or end town. I definitely agree with others, plan to arrive no less than day before, preferably more, to get over jet lag and get your bearings. If you can, add a couple days at the end of your tour to decompress.
Since you have AA miles, go to their website to check flights.
Have a great tour!