What I have enjoyed doing with Venice is liberty opening, to get a Merchant on the 3rd (I like to get the worker first) policy.
With a fairly straight B line to optics, you can have 2 puppets very early!
In my recent game, i started way on the south of a continent, isolated except for 4 CS's within trade route distance.
So I rushed 2 merchants, and with 2 triremes and 2 warriors, escorted them to the far corners of two other continents (there was a thin chain of islands connecting, it was a GREAT map, I'm using techtonics mod script).
With my 2 puppets, I was able to extend 4 trade routs to 4 other civs, way more lucrative than those 4 CS back home! I now have a far flung sea trading empire, Colossus of Rhodes, and 6 trading routs. I'm concerned what this is going to mean for border security once I start bumping up into these civs, but so far it's been a really low rex game (marathon/prince, I think prince might be too low for the map type or something, which is kinda snaky continents.) It's 200AD and I'm ahead in population with 1 Capital and 2 puppets!