venice, florence, rome, sorrento, amalfi coast, bologna, naples...pompeii, tuscany region, and on and on
So, before you get to such fine details as north-to-south versus south-to-north, lets do the math for a second.
You have 10 days, and 10 locations before you even get to "an on and on!" When you decide which order to do them in, I suggest you plan a visit to a hospital after you've blown through about 6 of these places, because at the pace you're planning, you will be in serious need of some medical attention.
To put it gently: your plan is not realistic.
You have 10 days? First of all, is that 10 full days, on the ground, not counting your arrival nor departure days? If so, then you have time for about 3, maybe 4 locations (if it's "10 days including travel" then you have enough time for 2, maybe 3 locations).
Your enthusiasm is charming, but I suggest you start by being sober and realistic. Please post your proposed arrival and departure dates - that is a prerequisite before anyone can give you more specific advice about an itinerary or route.