Welcome to the forum.
You have chosen to start with one of Ageod's most challenging games. In one sense this game is deceptive about the challenges because unit density is so low, but the complexity of good play is elusive.
Are you building forces with units integrated into a commander? And are you getting your stacks so they have no command penalty? If so, then you are ready to face the deeper challenges.
It is a good idea to have a plan focused toward the capture of objective cities. But a key to doing this is keeping your army supplied. Cities only provide supply up to the number in the city. This supply is based upon the components in a unit. So if a unit has four elements, it needs four supply points to maintain supply. Look at the total number of elements and the total supply values. Your first battle is keeping your armies fed.
You can expand supply in two primary ways:
Being in cities adjacent to other cities. In this game you draw supply from the city you are in and any adjacent regions, but no further.
Build deports. Because of shortage of money, you must be very judicious in where you place depots. Often inside cities is a good placement as they build the intrinsic supply value of the city, but it is still cheap to defend.
Once you master supply you are ready to take on enemy forts and cities. In summer is best, but if you must sieges can be done in winter; however, you need to think of what your supply wagons are doing for you. If you are the attacker in a siege you cannot draw supply from surrounding regions so you must have a chain of wagons going back and forth from cities you own where they replenish to your army.
Are you using the requisition and contributions cards? These are the primary source on income in this scenario. In longer scenarios you gain taxes and can ask your sponsors for donations as well has using diplomatic overtures to bring other states to support your side.
Yes, wait a few turns unless you see a city with a level one fort you can take without a breach. In the spring, campaign in earnest. EP are another kind of cash as they pay for all these initiatives including trying for a breech.
You can probably reply and say you have figured all this out which you mastery of the mechanics implies, in which case, some other ideas will be coming for you.