The only thing a mid-range gaming card gets you is the ability to run games, not an improvement in 2D display. Any modern card that has DisplayPort, Dual DVI, or even VGA can run your monitors. Here's the spec page
from the HD 6450.
That's almost true but not quite. Some low-end card ship with useless memory bandwidth, and with those you can indeed get into trouble just for running aero. This was at least the case with HD5450 where some manufacturers decided it would be a brilliant idea to ship with 32bit ddr2, and as far as I can tell there are HD6450 around with very low-clocked 32bit ddr3 where aero might be equally problematic. Needless to say such memory configurations drop performance way below that of any of the more modern IGPs (as they have only roughly 1/6 the memory bandwidth of your typical dual-channel ddr3-1600 configuration), they might in fact not have enough bandwidth just for display scanout (at least with multiple displays), leading potentially to display flicker (a 4MP display needs roughly 1GB/s bandwidth just for scanout, and those ubercrappy cards have only 4GB/s - that might still work but probably not with 2 displays, as you will get errors way before you consume all bandwidth just for scanout).
Oh and that bandwidth figure for the 6450 is only for the gddr5 review edition. I have never seen a single hd6450 card for sale which has gddr5 memory (though supposedly at least sapphire makes one), typically you get 64bit ddr3-1333 (for ~10GB/s bandwidth which should be enough to run aero but really drops performance below that of HD4000 (and possibly even below that of HD3000)).
So for just running Aero I'd highly recommend using IGP instead of getting such crappy cards. Note though that with intel igps for that resolution you need to use a board and monitor with displayport connections, since intel's dvi outputs are all single-link only and therefore will NOT work (same for hdmi). Well it may or may not work with VGA (not sure there but in theory it could) but clearly you really don't want to do that.
But yes HD6450 and GT610 should work fine too, provided they've got 64bit ddr3 (ideally with high memory clock but you're lucky to find either one with reference clock the manufacturers save every single penny they can) memory.