Hi Herf,
I traveled to Rome (twice so far) with no issues of theft or pick pocketing.
This past year, I rode the Metro (late day) from where I was visiting back to Termini - I was not worried. I kept my bag in front of me.
You will see a lot of scooters - either for recreation or people using to and from work. As far as I know, there has not been the "old issues" of scooter riders riding and grabbing your strap or bag. Just keep aware. If walking along a street that has a lot of scooter activity, just keep your bag on the inside. But, I really feel you won't have to worry.
At times, I rode the infamous Bus #64 and the Express #40. Bus 64 will get/be crowded. If a bus is super crowded, there are always more following - Bus 64 and 40 are very popular. So, if you are not really strapped for time, just wait a few minutes for the next one.
Validate your bus ticket, put it in your bag - Inspectors have been getting on at random stops to check tickets. If you don't have it when they check, you may be fined - a lot. Again, keep your bag in front of you, zipped, and maybe a light hand on it when stopping at stops to let peeps on and off.
If by chance, the ticket validating machine is not working, write the time/date/bus stop/bus # and bus ID # on your ticket to protect yourself. Maybe take a picture of the invalid machine.
For my out and about during the day, I carried a Kipling tote/purse (about 14") to carry essentials and for little things I may have bought. Kipling is very lightweight too, has good, adjustable straps and holds a ton.
I carried some day money in a mini wallet which I secured to the key fob in my bag. My first trip, I wore a money belt and the Kipling tote. Money belts are recommended - used for extra storage and put under your clothes. This past trip, I wore a mini Hedgren cross body under my coat to carry my passport, extra money, tickets, phone, etc. Hotel keeps the key.
I never took out my wallet in public or in a store. Since I had the strap attached to the key fob, I was able to keep the wallet in my bag and "just take out what I needed" at the register or whatever. Don't hang your bag on a chair. Don't keep your phone visible on a table or counter. Of course, these are all common sense things. I'm sure you know.
I think you'll be fine. In case of anything, there are many police and military around - almost every corner.
Termini Station - some people are okay with it and some don't like it. I had no issues. It is a madhouse, no getting around that. Again, keep aware. Yes, there are "random people" wandering "looking for targets." There are police walking around Termini (inside and out.)