Typically I have one main city island that has most of my production. I expand to other islands when I need resources. Also usually make one island that's farmers only after unlocking the commuter pier so I can upgrade my main island to be at least workers and above.
You shouldn't have to worry about min-maxing your production lines IMO. Just make sure there are enough warehouses to move goods. It's always cheaper to make more base level warehouses than it is to upgrade one for more cart guys.
Familiarize yourself with the production graphs located in Ctrl Q or the little graph button when clicking on a particular resource/factory. It will show you how much of the product you're making vs it's demand, and show how much of the production materials needed you have.
If you're having trouble, start a new game without AI. It takes a lot of the pressure off and you can expand at your own pace.
Don't be in a rush to upgrade housing tiers. I like to make sure I've wholly satisfied the needs AND happiness of each citizen tier before upgrading. Full happiness housing generates a lot more money than ones with missing wants.
Artisan and especially engineer production lines are very expensive upfront. It's worth it to build up a good population of artisans and let your income build up a bit before moving into engineers.
Engineers add power and tractors (if you have Bright Harvest DLC) which will make it so you do a lot of reorganizing of your industry and farm production.
There's probably a lot more to recommend but that's what comes to mind for now.
Oh yeah, sell soap to the prison island man. He needs it to drop in the showers big time.