You're going to find lots of conflicting answers because there really isn't one.
Rolling bags vs convertibles? This really is personal preference. Those who like convertibles will tell you that wheels are bad on cobblestones, lifting on and off trains can be a problems, they are heavier, and if you plan to fly on any discount airline in Europe, chances are they may not be allowed.
Those who like wheels will say it is easier to get around, you don't have to lug extra weight on your back, and you can attach a second bag to the handle of a wheeled bag.
Then there is your third choice--a convertible bag with a separate cart. Samsonite makes the "Micro-mover" which can easily fit inside a 22x14x9 bag and weighs about 2 lbs. I tried something similar once and found the bag and cart would topple over if I walked quickly or turned corners too sharp.
So, really, the choice is yours.
As for a day bag...most of us carry one. Usually either backpack style or messenger bag style. For me, the daybag fits into my regular bag (a convertible) on travel days. Others, keep them separate.
It's not really important what type of day bag you have, what's most important is how you carry it--especially in Italy. And that has been the subject of numerous threads on this board.
Oh, and wear a moneybelt.
Now after all of that....if you can handle it, I vote for using the Ebags Weekender.