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How do I decide which ARM board to go for if I am aiming to use it as a micro-controller to run sensors, actuators, motors, and solar panels? And I wish to power up the board via Li-ion battery pack.
Based on my personal experience I would suggest you to start with a simple development kit. If you plan to have WiFi or Bluetooth buy one that has already the module in it (it will remove a lot of pain ...)When you have your dev kit in your hands and a decent screen (LCD, OLED or E-Ink) you will start to create your prototypes in mbed OS and trust me that part takes a lot of time.
When you have a stable prototype with your development board and you tried different sensors (sometimes you buy one motor or sensor but it is not the one you though) you will have more experience and being able to choose a more advanced or specific development board.
Only when your dev board is doing what you though you can try to design your PCB, outsource the creation and try it again with your mbed OS firmware and the sensors
I would kindly suggest you to not follow the path of choosing an expensive board as the first prototype because most of the time you realize that you need less or more power and other things like more connections, memory and so on.
I think that starting with a dev board like the RF51 is a good start, plenty of example available, Bluetooth out of the box and plenty of flexibility