Echoing the comments about passports, as the hotel will take your passport, scan/photocopy it and if you need it you’ll need to ask for it - typically the next day is fine, but they always seemed reluctant to simply take a copy and return it whilst checking in.
If hitting the top tourist destinations, Rome, Venice, Florence, Pisa etc. or places like Naples/Palermo, then it is worth extra vigilance against theft, Be especially wary going through these train stations and in places where large numbers of transient visitors pass by e.g. tourist hotspots, especially when it is bustling busy. Conversely in quieter & less touristy locations, there is less cause for caution.
Some travellers swear by an under-shirt ‘money belt’. Slightly awkward / uncomfortable, but should give peace of mind.
Most of the places I go to in Italy avoid the perils of the major tourist hot-spots, so I’ve felt pretty confident treating money and my wallet no different to at home. On the very rare occasions I’ve felt a little twitchy, I’ve either left money in a hotel / apartment safe, or kept the majority of my money separate, whilst keeping ‘readies’ in a more convenient / natural location e.g. a trouser pocket. I’ve never been pickpocketed in Italy, nor have I seen it happen, but I have heard of it in the locations mentioned above.
As well as money, have some care over sign-posting yourself as ‘rich/easy pickings’. Likewise beware of scenarios where your valuables are in your bag but out of sight. Handbags over the back of a chair or smaller bags stashed at the end of a train carriage are examples that might prove enticing. We do always try to ensure that both of us have at least €20 on us, as should the worst ever happen, at least one of us has the means to get us back to the apartment/hotel.
One useful tip. It’s very natural to pat your wallet just to check it’s still there. Apparently this is quite a useful signpost to the pickpockets! If you’re going to do so, be subtle!
Slowtrav had some useful hints / good discussions a while back, so worth a search there.
Finally… hope you have a great trip to Italy. It is a place we return ~ once a year, and it really does reward return visits. There may be a temptation to try to see ‘everything’, but that’s impossible. Take your time to enjoy what you do see and anything you can’t fit in is merely an enticement to return.