Best transportation method in Sicily

It's hard to give general advices since you didn't specify your itinerary but here are my two cents.

If you only plan to visit the main touristy cities you shouldn't have any problem using buses and/or trains. Remember, in Italy the trains are available almost everywhere and it's usually a very convenient method to move around; Sicily is no exception. Finding information about buses can be tricky because most of the sites are in Italian only but the interface is usually quite simple to understand and doesn't require and extensive knowledge of Italian. You can also ask for help planning your next stop at the front desk in your hotel / hostel they are more than glad to help (provided they speak a little English)

Buses

• Azienda Siciliana Trasporti (AST): this is probably the most useful in order to find buses but it's also the buggest one, as on now many pages do not work but thankfully the one with the timetable does work (click on the Linee e Orari link)
• Sais Autolinee: click on the Prosegui button and you'll be presented with two dropdowns, the first one is the departing city and the second one is the arrival city.
• Etna Trasporti

Train

• Trenitalia click on this exact link otherwise searching for ALL trains, instead of just the new and fastest one which are not present in Sicily can be tricky).

On the other side, the car gives you way more flexibility but this is very subjective.
I travelled in areas where public transport were way worst than Sicily mostly because, as you said, the public transport is better to meet people, especially if you are travelling alone. Using the public transport requires more patience and it's less comfortable but it pays back in form of social experience and funny stories to tell back home. It's all up to what kind of person are you.

EDIT [just read the comment in which you say you are 7 people]

Travelling in a group of 7 requires a little bit more of planning if you intend to use public transport because on a busy day you may have a hard time find seats last minutes. With 7 people public transport could also end up being more expensive than just renting a car.
Driving in Sicily is not that bad, unless you are used to 7 lane motorways and automatic transmissions. Old cities can have small streets and may requires some skill to move around flawlessly but all the big cities (like Messina, Catania, Agrigento, Palermo ecc) are absolutely up to european standards.

Italian speaking here: RENT A CAR.

In Sicily (and generally speaking, southern Italy) you can't count on public transportation: delays, strikes, cancellations happens every day.

During my latest trip to Sicily (2013) I rented a car with EuropCar and everything went fine.

Just some notes on safety:

• Don't know where are you from, but in Sicily they drive as crazy!!! Watch out! :-)
• Remember to note and report every damage not listed in the receipt when you first get the car AS SOON AS POSSIBLE.
• As said by rental agency people: in big cities (especially Catania) pay for private and secure parking by day and night (Siracusa is way safer as far as I can tell).
• Get down of the car when you make fuel: look after the guy that is making fuel to avoid any scam.

Have a nice trip!

I used public transport (bus) in Sicily and travelled to quite a few places (Palermo, Monreale, Catania, Etna, Taormina and had no problem whatsoever...

Back from Sicily, renting a car was definitely the best advise especially for people interested in natural sites. Some major natural sites are indeed not accessible if you do not have a car, or they are only at some times.

• For the Etna, we were lucky enough to be present during the eruption. But you only see it at night when there is no more buses. There are some excursions, but they are very expensive and only a few times a week.

• Maybe I missed it, but sites like Cavagrande de Cassabile or Pantalica are not accessible by public transportation. Note that Cavagrande is closed until 2015, but there is another access point from the North (car needed !). For Zingaro there is a bus.

For the cities and cultural sites, public transportation is OK. Sometimes hard to find the good stop, but relatively frequent frequent and on schedule. There is hardly no information in the small bus stop, so try to get to the terminals in order to get proper information. As a remark, I did not try the train, but the buses where full of tourist.

As several people warned me, driving in Sicily is... special. There are many motorbikes in addition to the car, and in some places it is just crazy (especially in Palermo, where I saw 2 motorbikes and 3 cars on two lanes).

Car parks can be quite expensive. there are also "free" car parks where some"guardians" ask for donations. But we had no difficulties to find parking places.