I am responding with the assumption that you are just getting into GTD. Apologies in advance if this is not case.
First, priority is the last consideration you are supposed to use when determining what task to perform next. The emphasis is on contexts - not priority. I suspect your list of tasks is overwhelming because you still have some more work to do with contexts and/or because you haven't grappled with identifying those projects or tasks that really should be deferred for later. You need to put a great deal of thought and effort into refining your contexts, and (at least in my case) even more effort into honestly identifying and dealing with tasks/projects that have to be deferred. The payoff is manageable task lists when using the Context Mode.
FWIW, when I first got into GTD I struggled with deferring tasks/projects where the only person with whom I had to negotiate was me. In contrast, it was relatively easy to review project/task lists with my various stakeholders, and negotiate their lists to something that was actually doable. Your mileage may vary of course!
What is great about OF is that there are several ways to deal with deferred projects and tasks. You can place projects On Hold, and review them during your weekly review; or you can create special review folders for projects or tasks that you only want to review monthly, quarterly, annually or whatever period works for you (the "someday/maybe" group). Single-Action tasks can also be deferred by setting an appropriate start date.
From a GTD perspective, due dates are for hard and fast "the universe will end" deadlines. Therefore, you shouldn't be trying to enter due dates unless there is a compelling reason to do so.