Some shops (especially high-end shops targeting tourists) will ship; others probably don't want to be bothered. Shipping costs on heavy or bulky items will probably be a lot higher than you are expecting. However, on expensive items, you may save enough by shopping at a store that doesn't charge VAT on exported goods to offset much or all of the shipping cost.
You need to be careful about buying things you cannot carry away with you. There are occasional reports of fraud, with the object you selected and paid for not being the one shipped. For expensive purchases, it would be worthwhile to Google the name of the store as a precaution.
The Italian postal system used to have quite a bad reputation; things went in and were never seen again. I have no idea whether that situation continues; I hope not. In any case, you should be sure your shipments are insured against loss and theft.