I would like to move to Italy. I really

You could try a web search "casa affiti lucca".

Villatua is an English-speaking real estate agent based in Lucca. I am sure that they will be able to help http://www.villatua.com/rental_home.htm

Hi, Lucca is really nice, so are other areas of Tuscany, I rented a nice place just 20 minutes from Florence, they offer long term furnished rentals from 4 months or longer. could be handy, while you're checking out different areas and testing the water.They're English and were very helpful.  http://www.ciarpaglini.net/index.html    If you're looking for a rental on local market you mght need some basic Italian, also Italian rentals tend to be 3 + 2 years contract - often unfurnished, so it's a good idea to get something for a shorter period at the start while you're searching for a real long term solution. Anyway good luck. 

Biddy that place look superb and we know the countryside is eveything you read and hear about - stunning area!