Skip mining asteroids or the moon

Mine the Martian moon, Deimos, instead.

Deimos is positioned perfectly for such a purpose.  It has a relatively low delta-v requirement from the Earth--- lower than a lunar landing--- and has a potentially large source of water and carbon.

That is a thought.  When you make methane out of mostly carbon sources, you will need twice as much water.  That's because methane has 4 hydrogen atoms per molecule, while water has only 2.  Plus, you need 4 oxygen atoms to burn the methane, so you will need 4 molecules of water that produces two molecules of methane.  That's more methane than you need.  Why produce the excess methane?  You have to unless you have an oxygen source.  If there's plenty of carbon dioxide on Deimos, then that could be the source.  But if there's just a lot of elemental carbon around, you are going to wind up producing an excess of methane.  That excess can be exported back to the Earth-Moon system.

Since both the Moon and the Earth have large sources of oxygen available, you just put those two sources together for a fuel transportation system.  From the Earth, a LOXLEO system obtains the oxygen.  From the lunar surface, you can obtain plenty of oxygen.

The excess methane from Mars can be sent back by ion propulsion.  Methane makes up only 1/5 of the reaction mass, so this is a big advantage.  Thus, a relatively small mass of methane can be sent from Mars that will enable landings on the Moon, and transits back to Earth.  From the Earth, the oxygen obtained from the upper atmosphere will allow transits back to the Moon, and from there to Deimos.

Once you arrive at Deimos, you have an excess source of methane which can be used for powered landings on the Martian surface.  Furthermore, you can make methane on the Martian surface.  No need to carry along so much fuel.  That should simplify transits to Mars.

Bringing an asteroid back to the Moon appealed to me, but it seems like a very time consuming project.  It may save a lot of time just to mine Deimos instead.  You would have to confirm that you can do this, though.  As far as I know, there are no plans to do this.

A launch window opens every two years between the Earth and Mars.  However, you can keep the pipeline flowing, the missions can be executed each time a window opens.  You wait for fuel, then when it arrives, take off for the Mars system.  You could do it on a regular basis without the need to launch anything but a crew from the surface of the Earth.

In addition, you could start a lunar colony with your access to the Moon.  The Moon has water sources, so you could grow food on the Moon, and that would be another thing that wouldn't need to bring from Earth.

The same thing could be done on Mars.  So, there's two things you could do to simplify missions to Mars.

Update:

I was for the mission to bring an asteroid back to the Moon and studying it for the possible purposes of mining it for water.   Instead of doing that, you can go to Deimos instead, and do the same thing there.  It is like an asteroid, and it could be the key to opening up colonization of Mars.