"Just me, but I think NEOs should be our first priority because their resources are so much more accessible than the Moon or Mars. "

Much more accessible by whom?

Do you want NASA to mine asteroids?

Should the nation of China, Japan, or US mine asteroids.

What do you mean by accessible?
For example, if one is looking for accessible resources, I would say that methane hydrates in Earth's ocean are very accessible as compared to NEOs. Should methane hydrates extraction therefore a priority in which tens or hundreds of billions of dollars of tax payer money are used?

And accessible to whom and where to?
If the destination of resources from NEOs is high earth orbit, then the overall delta-v cost could be significantly lower from NEOs.
But I would contend that to extract NEO resources one first REQUIRES a market for these resources BEFORE attempting to recover resources from NEOs. So you need a market in high earth orbit and the question of importance is how does one go about getting a market in Space.

Unless you mean the destination of these resources from NEOs are to be to the Earth surface which has a mature and established markets from a wide variety of things. If that is what you mean, I don't think one can say that NEOs are much more accessible than the Moon or Mars.

Next, we get to specifics on resources.
I think what is first needed in space is rocket fuel.
Cheap rocket fuel in space will allow more access to this solar system. And dirt cheap rocket fuel in space is somewhere around a million dollars per ton, whereas this is not a cheap price of fuel fuel on the Earth surface- it's a thousand times more than a reasonable price even in pricer areas of Europe or Japan.