Where in Italy do you live? Do you speak Italian well? Being able to speak the language is VERY important and will mean you will be far more easily able to locate raw animal foods you can afford.
The problem with Italy is that there is not enough arable land so that some meats, like beef, are a bit more expensive. There isn't any real organic or grassfed meat industry in Italy as yet. However there are certain online organic sources/directories:-
http://www.biobank.it/en/indexBIO.aspAll that said, maybe I ought to give myself as an example, so as to help you a bit further:-
I know almost no Italian, so, when I go to my Italian home during the summer holidays, I often run into difficulties. In my town in Liguria, I have access to a fish-market which has a lot of very expensive raw seafood(some of which goes up in price by 50(!) euros per kilo as tourist season approaches - unsurprisingly, the market is Mafia-owned). However, it has a lot of very cheap raw seafood as well(less than 5 euros per kilo). I don't always like the taste of the dirt-cheap fish much, admittedly, but they're fine as a substitute, and I also buy a bit of very expensive swordfish here and there. The fish is mostly wildcaught, not farmed, except for the salmon, and probably the shrimp/prawns.
In the past I used to buy raw tongues from local butchers at 17 euros per kilo. Those tongues are tasteless since the cattle are fed on a lot of grains, not recommended. I have since bought raw horsemeat from local horse-butchers(cavalheria). The horsemeat from cavalherias costs anywhere between 4 euros to 20 euros per kilo. More usually, I find meat costing between 7 to 12 euros per kilo, when I go there. I always buy the cheapest meats there, as I find no difference re nutritional quality between different cuts of meat. Now, the horsemeat tastes much better than the grainfed beef tongue I used to buy, so I am guessing that the horses are mostly raised on grass, though probably also on, I fear, some oats/grains.
I live close to the French border but haven't heard of easy sources of meats. I am aware that there are a number of small-time grassfed meat French and Italian farmers in the hills away from the coast from whom I could buy sheep or goat carcasses, but I would need a car/driving-licence and the ability to speak Italian, if in Italy.
I also used to prise raw limpets from the coast where I live, but, sadly, the supply has vanished, I fear due to pollution from boats. I still scavenge for raw eggs from female sea-urchins as they taste amazing. Going harpooning is a waste of time, though, as the area is over-fished like most of the Mediterranean, so only tiny fishes exist right next to where I live.