The best services to use when moving to Italy

Well said! We have found out the hard way, even moving thinking the problems were very localised.
It's the English people employed by housing agencies that I can safely say are the root of the problem. If you are blessed with some intelligence and observe things that they should not be doing well that's it, they use a variety of ways, mainly by discrediting you to locals, and if living in a small place the loveliest of the locals will believe the English charmer. But it seems the patterns of behaviour are the same in a bigger place, will follow similar tactics, but due to more people spreads their poison in many ways. There are a few still untainted, but not very nice to be on the receiving end. I now understand why many expats local to here keep together to socialise, but even some expats, who have probably been at the receiving end of dishonesty, etc., do not talk about it, probably wanting not to look stupid, and also due to lack of ability to earn good money here, steal your ideas.
Despite all of this, I love Italy and the few Italian friends I have, and have to struggle when a certain person from an agency continues to sabotage mine and my family members quality of life here. Setting out always to keep discrediting, creating a situation that if this person were to be accused of something, we would not be believed.
My advice folks if embarking on the dolce vita:
Trust no one from an agency with English speaking worker. They might be great, honest and working in your best interest, let them earn your trust over time. Don't be charmed.
Keys: change your locks and security, even if living here full time. Keys seemed to have been abused in our situation. Be careful who you leave keys with if you are away, again trust needs to be earns.
Ensure before the final act that all items in your house are there just before you sign.
Learn the lingo fast as you can
Question how much for the agency to provide a service re connecting utilities. It's not much to do yourself, especially these days with the internet. It takes a bit of work with google translate, but most things you can do yourself. Some agencies provide this, don't pay silly money.
Translating, do this yourself where you can, however important things like legal stuff, pay someone independant, a professional, not someone trying to earn a few bob, my trust has been broken twice re this.
When you get your documents back after the signing, make sure the land you thought you had bought is on the deeds. A snap shot of the original sale is a good way to go. Also double check on the day of signing, don't be rushed.
If employing a builder ask your local commune for registered builders, you can be prosecuted for not doing this, and ensure all the names on the contract you sign before work, are named on the contract.
Basically, don't be a mug, have eyes in the back of your head, check all documents. Get over these hurdles and get confident in your own ability to sort things out and you will survive, but you may not be popular.
I still love Italy despite all of the bad experiences. If I had to leave due to Brexit I would be mortified. So if you are made of strong stuff, you can weather the initial storm. Go for it.  I just wish I never spent my life savings coming here!but despite corruption and bad experiences, this feels like home, it's like falling in love with someone and sticking with them.