Hi there,
I am still a beginner, but i think it can't harm to throw my 5 cents in here. Feedback on the following tactics is appreciated. Hope it will help some you, too.
I think speed is very important in this game. By that i mean your very first actions, which are unfortunately also the ones that are most influenced by the random number generator. Every action (even lifting some fog of war) should be made in mind with its purpose. Ideally every action benefits the following as much as possible. It's not easy to explain for me, so let me give you an example:
A basic way that a follow-up action is influenced is a basic could be your first move where you scout a Trade House, so that you then are able to infiltrate it. Not much leeway for creativity here. (Of course there are other first move tactics...)
At the latest in your second turn it might be worth considering which district to scout. Maybe you want to scout a district that allows you to reveal a policemen in the same turn, which you can then pick off with your gang to level it up. The important part here, is not wasting an action point of your Master Thief. You will want to discover this guard as a side effect of an action that is supposed to advance you to another goal. Those are very scarce and very vital in the early and mid-game.
Another aspect not to underestimate is economy. Make sure you get income (Lanterns and Gold) as early as possible and if you can manage it, disrupt the enemies economy without spending too much resources. (e.g. buy the saboteur and bomb their Trade House). Every round you get income lets you expand more quickly. Orphanage is great to get early in the game, because it reduces the cost of your income generators (urchins). Also put one urchin in each church you find. Do not underestimate this one coin per round - if you can keep this church for more than three round, that has paid off and later you can skim a victory point.
I could go on but i really need to get to university and work on my bachelor's thesis. Hopefully, i can write more soon. Enjoy your thievings.