Well, an IDE is a generic name for a kind of software (IDE = Integrated Development Environment). There are many IDEs out there, the Arduino IDE is what we mostly use for Arduino development. Microcontrollers are usually programmed in C++, not Python (if only because Python is interpreted, so won't do well on a small controller).
For your project: you first have to write down exactly what has to be done, from a high level perspective. What inputs do you want (you're talking about linear pots), what outputs do you want (some kind of solenoid), and how does the output have to react to the input.
One input controls one solenoid fully independently? Or are they interdependent somehow? How so? Do the solenoids have any feedback loop as well?
This are some very essential questions that you must have answered before you can design your system.
When you know WHAT you've got to do, you can start thinking of HOW you're going to do it. Which exact solenoids do you need for the amount of flow (liquid? Gas?) and the amount of control you need?
Then: which controller is suitable for that solenoid? Fair chance the manufacturer has suggestions, maybe it even has controllers built in, making it easier.
Power supply comes in play. You probably need a pretty serious power supply for those solenoids - that's some 14A when all are engaged.
Look at the inputs; which exact parts do you have? Again, do inputs affect one another or are they independent?
If there are eight fully independent units, build them as such. You end up with eight microcontrollers in the final product but those are cheap, and it will make development easier: you develop one, and then just copy another seven times. If interdependent it becomes a lot harder.