Newer 172...
I understand that this would be your first aircraft, it also seems that money may not be an objection.
I owned a 2000 172S, nice airplane as a training aircraft but that is where it ends.
In that category, but with a much better performance for the same fuel consumption you could get a 2007 or newer Diamond DA40, the XL can be had for about 200K US, it has a 145knot TAS performance and it does it in about 9 gallons.
I have a 2005 DA40, same engine but a lousy A/P
buy the plane that fits the mission, your mission now is training I think! Rent dont buy for know.
Good luck