My (personal) advice would be: don´t spend all your money in the first turn. You´ll need to pay your armies for a couple of turns and the income from your provinces isn´t enough. Plus, unlike in vanilla M2TW you won´t be able to rise the taxes, quite the opposite, in a number of cities you´ll be forced to lower them.
Try and find out which cities have the greatest income and place high chivalry/dread characters there, that´ll allow you to raise the tax level there. And even if not, being able to keep "normal" taxes in London or Oxford will yield more than "very high" ones in, say, Flint or Pembroke (to take an extreme example).
Where you can, build Merchant wharfs, but don´t waste money on other trade improvements in the first couple of turns.
Think very carefully about some units to disband, army upkeep is your biggest problem, but also consider that within a couple of turns an all-out war will break out and you´ll need troops.
Once you´re at war, sack and ransom. Don´t end a battle as soon as the message pops up, but use your cavalry to take as many prisoners as you can. A hefty ransom has financed more than one campaign for me. Consider this tactic carefully when you´re using generals with a good chivalry rating, you´ll likeyly get the "winning first" trait, which will lower chivalry. With a dread general (Prince Rupert, for instance, if you´re playing the Royalists) you need not have such qualms, quite the opposite.
You won´t be swimming in cash in this mod and you won´t see many "green" cities either. Be glad for yellow, accept blue, they´ll be a common occurance. Castles mostly loyal to the opposite faction are a real pain, since you can´t build printing presses or coffee houses there, so you might consider leaving them alone or to exterminate them.
Watch your generals. Loyalty is rather low in this mod, so be carefull to place them into cities or camps as much as you can, otherwise they might desert.
I´m note sure how to get them to "feel appreciated" (winning battles seems to help, though), so I can´t give a lot of advice there.
That´s it, the quintessence of, by now, five campaigns with Parliament and Royalists alternating. There might be other ways to manage, but this is what I´ve found to work best for me.