I play Venice a good bit on Immortal level. I don't consider myself an expert by any means, but I've had some success with the following approach. I don't take a rigid approach of first build this, and then build that, etc. However, here are my rules of thumb. First off, I'll say that you can have a pretty hard time if you don't have a number of nearby city states on decent land. Until you come up with an approach that works for you, I would suggest that you abandon a game if you don't have nearby city states on good land.
Pretty quickly I research sailing and optics for two reasons. One, you obviously want that Great Merchant (GM). Second, if at all possible you want to build the Great Lighthouse for two reasons: 1) It gives you one point per turn toward the generation of another GM; 2) That +1 movement for your ships is of value. About 50% of the time, an AI civ will beat me to the Great Lighthouse, but I think it's worth trying for the chance of getting a second GM earlier.
I usually do not send out that first GM to buy a city state until I have researched bronze working. My reason for that is that you usually don't get iron near Venice, so if a city state has it, I might buy that city state, unless it is one of those all or almost all tundra city states that don't grow well. Once you research currency be sure to send a specialist to your market since that will give you +1 points a turn toward a GM. Also build the national wonder that gives you extra points toward great persons. (The name escapes me right now.) If you're on a river, be sure to build a garden for the extra great person point production it gives you.
As for policies, I work all the way through the Tradition tree. I then start working the Commerce tree, starting with the policy that gets you liebknechts, followed by the one that reduces the cost for purchasing buildings and units. From there I sometimes finish Construction, or switch to Science. It depends on my situation.
Early on, you want to grow as quickly as possible so concentrate on working those tiles that will increase your food production. After founding your first two cities, if possible start a trade route from each one to Venice that will deliver food. That will fuel the growth of Venice. You also want to generate as much gold as possible. That means getting your trade routes going as soon as possible. I almost always send ships in preference over caravans because they give you more gold.
I don't claim that this approach is optimal, but I hope it helps.