Hi Priscilla,
The best places to start looking for a job in Italy is either Milan or Bologna. Both cities are expensive, but they are the ones which can compare the most to European standards and the salary you will get (unless you don't accept any internship/stage/tirocinio contract) will allow you to live up to your standards. Rome is beautiful, but defining it chaotic would be an euphemism, also, it is difficult to find paid positions that do not imply terms of 'exploitation' (salary, conditions of work, etc.). But you may be the lucky one. Generally, if you wanna live in a more slow-pace and historical environment Rome may work too (but at least go visit it, it is amazing!).
Anyways, it really depends on what you are looking for. Milan is like big European Capitals: it never stops, and people work a lot; in Rome everything is late. Generally, any city in North Eastern and Western Italy works good as a quality of life and services offered.
Central Italy is good too, people are really nice and city centers are medieval and beautiful. You can check out Florence, Pisa and Perugia here. The South is amazing too, it is just that life gets a bit harder for a bigger number of people there, and many are forced to move up North. So I wouldn't personally suggest you to go there to work. Go there if you wanna spend good time with really good people. However, there may be some option there too.
For what concern your contacts with employers, I would suggest you to contact directly the company/firm/etc. of your interest, unless you are 100% sure the agency/ job hunt is a certified one and is not trying to trick you. Also, contact a job hunt if you want just to live a period in Italy, otherwise be aware that the taxes you will have to pay to the Italian State are high.
If you are looking for a long-term job Milan, Bologna and Rome offer you plenty of international/ multinational organizations (Rome) and companies so it may be easier for you to find a job and you won't need a job-hunt.
For what concern the CV, Italians usually include pictures but this trend has been gradually disappearing. A standard format for your resume works good.
As long as you dress up properly, you don't get too informal, and you don't talk about money, there is no particular requirement. I would say just be natural and don't speak out your mind excessively.
Last but not least, I think Italian language is something you will have to learn eventually. Italians are not known to be fluent in English, and despite in your workplace you may use English, to survive in some areas you will need a bit of Italian too.
I hope this could be of help!
Good luck.
Giulia