As you said in your question, I think the biggest factor that comes to play with what is important is the chronological order of some tasks that need to get done in order to move on to the next one. But, not every task will be dependent on the last one like that. This is where careful planning and creating an efficient work breakdown structure will be very helpful in visualizing what tasks need to get done more urgently than others. Some methods that can be used to rank the tasks that are more important could be to decide how much of an impact it will have on the final product. For example, a task such as speaking to the manufacturing company about how much the material that the product will be made out of will cost will be more important than creating an advertisement for the product that has not yet been created. This is not saying that the advertisement is not important, but rather obtaining key elements about the device before it has been created should have a higher priority. Again, in order to come up with these systems of rankings, it is crucial that the team is able to communicate effectively amongst themselves and come up with ideas that everyone can agree upon.

I agree with tgt6. The most important thing is when ranking tasks is to prioritize those that need to be done before other steps. Within that you should then prioritize which of those have a bigger effect. For Example: if task A needs to be done before B that should get less priority than task D that needs to be done before E, F, G, and H especially if those tasks will take a long time to complete. The goal is to essentially look at the knock on effects of each of the tasks and roughly calculate how long each string of tasks will take (meaning A and B or D,E,F,G,H) and prioritize the one that will task the longest. The you look at what other tasks can be done concurrently with those major tasks that you filled the schedule in with.

I agree with @tgt6 and @ac825. I believe it is very important to prioritize tasks that are needed for later tasks or are codependent, however, when tasks are independent of one another I think it is imperative that one considers the time and effort needed. Ideally when creating a Pert or Gantt chart, you want to optimize time, resources, and effort to simplify complex projects as much as possible. Therefore, tasks should be ranked in the order that yields the most efficient timeline and brings the team closer to their end goal. Does anyone agree or are there any additional factors that influence how tasks should be ranked that I did not mention?

While I agree with what everyone has posted so far, especially with the @mmodi stated regarding using a Gantt or Pert chart to create the most time efficient timeline, I believe that when ranking importance of tasks that you need to closely observe the customer needs and the DSD for the product. One specification may need parts A, B, and C completed before it can be accomplished and it provides high importance to those parts, another specification may not have any pre-requisite parts that need to be completed but is a more time consuming task that absolutely must be accomplished and work without issues. To summarize, I believe that while finishing tasks that are pre-requisites for other tasks is of high importance, it is just as important to first look at the DSD and prioritize the importance of all the specifications and work from there.

As mentioned above, the primary way to organize task priority is by which tasks need to be completed before the next task can be started. In the case, where two tasks are independent of each other and you have to choose which one to prioritize, I believe that whichever task is more crucial to the over completion of the product should be focused on first. For example, during my senior project two components of our device was the circuitry and the adjustable belt strap. Although they were not related to each other, they both were important to the final product. However, we decided that the circuitry component was more complex and we were more likely to encounter difficulties working on it. Thus, we chose to prioritize that since we felt that it was more important to get that done. Therefore, I feel that another factor that should go into prioritizing tasks is how important the task is to the overall product and what the likelihood is of encountering problems as you work on the task. 

the way i would choose the tasks by level of difficulty. if you have 2 tasks are not related to each other then i will pick the harder one to finish first. in case of i get frustrated and board on this task, i can change to the other one to get relaxed.  or pick the tasks by the time. start the one that is closer to the dead line.

Just as most have mentioned the most important factor is team communication and breakdown of prerequisites and necessary time to complete each task. After this timeline has been created a pipeline like a Gannt chart can be created to calculate the necessary time that the project will take to complete without losing time waiting for tasks that are necessary to move to the next step. A similar logic is applied when designing the algorithms for a central processing unit. Pipelining is used to ensure that tasks are completed in parallel and that the output of one is ready to be used as input for the next in the most efficient way with minimum delays.