Congratulations on getting the annual fees waived. We all love free stuff, don't we ;).
With Velocity points, you mainly have 2 avenues of using your points to get to Italy. One is redeeming Velocity points to fly Etihad/Singapore Airlines (Etihad involves high surcharge) and the other is transferring your Velocity points to Singapore Air Krisflyer program. Krisflyer charges a med-high surcharge for redemptions in general too.
Personally, I am not terribly familiar with Velocity international upgrade policy so some one else may fill in in the gaps of my response. Personally, I mainly focus on outright redemptions. Everyone's circumstances is different.
With Krisflyer, you have to buy an eligible Economy fare (usually much more expensive than the cheapest economy fare and if there are availability for Business outright redemptions, you generally get upgraded straightaway if you have sufficient miles (pts). Sometimes is worthwhile paying for Premium Economy fare because the difference in price with the eligible Economy fare is minimal and you would need less miles to upgrade from Prem Econ to Business.
Now, I can give you an idea of how much it costs for outright redemptions, for your reference.
SYD-MIL one way business
80750 Krisflyer miles or 203k Velocity pts. (75k Krisflyer miles for Econ-> Business upgrade and 38k Krisflyer miles for Econ-> Prem Econ upgrade)
To quickly accumulate points, credit card signup bonus can be one of the many ways to do this. However, please consider your own financial circumstances. Check out Point Hacks articles on how Credit works here link.
If increasing points earn from monthly spend is your strategy of choice, it may be worthwhile finding a credit card that earns you more points per $ spend. Check out the Point Hacks master credit card table here.
Good luck. Hope it helps.