RESOLUTION DOES NOT MATTER
do you see doom 3 at any resolution struggling to play on any modern card?
i can't tell if you're joking or being serious...regardless, OP has listed some modern games, and resolution most certainly has an effect on performance for these games.
For 1440x900 will be more than enough, but if you have the money to put into it, there is really no reason to go with a lesser card. You will still need the shader power regardless of resolution, and if you ever decide to get a new monitor then you will be kicking yourself if you didnt get the best card you could.
As for whether you will be able to play those games listed on max settings, I'm pretty sure the 6870 will be just fine at 1440x900, but if you go up to 1920x1080, then you may find that even the 6870 will struggle on max settings for crysis and metro2033.