Acceleration causes increase or decrease in velocity, whereas applied force also causes deformation. No acceleration can therefore be understood as the absence of acceleration, whereas no net force may very well be a lot of force. The 'no net' aspect of it merely meaning it doesn't result in any acceleration, whilst it may still result in deformation.
So when it comes to a 'What came first, the chicken or the egg?'-like question, the answer is clearly force, since force can exist without acceleration, whereas acceleration can not exist without force. Anyone with experience in constipation will be able to explain that to you.
The reason this is still a load of BS is the fact that it matters whether or not get your facts straightened out before you ask a question like this. The beauty in scientific formulas does not lie in the formulas themselves, but in the fact that the image they create perfectly matches reality. You can't just forget a screw and hope it still works, unless you are Roger Penrose and you're busy delivering mathematical evidence for the fact there is no such thing as mathematical evidence. The notion of the force you present is a net result of any (not given) complexity of forces, whereas the notion of acceleration you present does not take into account that, depending on how you look at it, the whole universe is nothing other than a bunch of accelerations. You know, Big Bang and all that. So on the other hand, an acceleration may be a real thing, but a net force is by its definition always an effect of the process of the 'netting' of other forces. It doesn't exist unless you make it exist. Following that line of thinking, its the net force that is the consequence and the acceleration that's the cause.
The interesting thing about this question as is, is in its paradoxicality. We still have to figure out how to shed a light on traveling faster than light in respect to which putting two and two together so far doesn't add up. After looking at things that are natural or real or complex, paradox is the logical next subject of interest.
We know that by looking at things, we change them. What we know very little about is how we change them, depending on how we look at them.