Greetings dear friends and servants of the Queen of the Adriatic.

I've just finished one VH/VH long campaign as Venice.

My advice for a good start would be:

1) Buy Bologna at turn 1 (costs around 5000/6000fl)
2) Send a diplomat to the Pope right away to get an alliance and give the Pope-o-Meter a boost any time you have the means to (Florins and/or map info and/or settlements you can't afford to keep atm).
3) Prepare 2 stacks of armies to siege Milan and Genoa in a short campaign, in order to minimize the rep hit with the Papal state.
Wiping out Milan faction should be your the first objective, letting them live makes them become every turn a bigger threat.
4) Grab with your remaining forces all rebel settlements you can, listed by order of importance: Florence, Ajaccio, Cagliari, Durazzo.
5) Give Durrazzo to the Pope if the Byzantines show up in the area with a stack of armies. (This will prevent early war with them and allow you to be able to defend against HRE in the meantime).
6) Try to secure an alliance with Hungary.
7) Take care of Sicily the same way you did with Milan (1 stack per settlement, blitz style).
8) Be prepared to defend Zagreb from heavy HRE assaults.

You should then now own all Italy and have a quite nice Florins income allowing you from this point to continue on the campaign in whatever direction you fancy.

My advice for continuing the game would be:

1) Take every Mediterranean island if possible.
3) Don't seek to expand to the East too far for Mongols and later on Timurids will show up and will turn your investments in a loss. Using the same strategy than the one to defend Zagreb should be used in Constantinople that should be considered as a "Frontier city" filled with full stack or armies).
2) Build up solid and consistent fleets. (Each fleet has a max range/per turn then each of your fleets should touch the max range of the next to it in order to be able to intercept every single enemy fleet that dares enter your waters).
3) Seek to "Envelop" the Mediterranean see to create new trade routes between your settlements and boost even more your income. Coastal settlements all around the see should be of interest for you (Exception made for Middle East).
5) Don't try to keep and hold inland settlements unless necessary, they will cost you more to defend than what they will reward you. For example create safe borders to the North by creating "buffer zones" by seizing inland settlements and handing them to the Pope.
6) When you'll be invading the Iberian Peninsula, use the blitz method. The settlements are far away from each other. Beginning the invasion without sufficient backup will make the campaign last much longer than it should.
7) Try to obtain an University asap for the "World is round" event is triggered by the construction of the first one. This will allow you to send and expedition early on and able you to use Venice famous merchants at their best (one experimented merchant on Tobacco or Cocoa resources will reward you thousands of Florins each turn).
8) Have fun.