Well... what exactly IS your budget? I mean if it is open ended you could throw in 2 GTX 780 TIs, but I am assuming you don't have nor want $1400 to throw into graphics when you're playing at 1440x900
A 7870/R9 270/GTX 660 (Ti optional) would probably be good for you though.
i mean like below $100 price range dude
You said you were a high budget user... I am going to guess that was a joke!!
Sorry my friend, you cannot get near ultra quality, even at your resolution, with a $100 GPU. You could probably do medium-high at 30 FPS with a $150 GPU, but you cant max out games for under $100, really on any resolution if it is a triple-A game. What games are you interested in playing and maxing out?
you can run ultra detail settings just without AA and AO at 30fps easy, very easy, with a benjamin. there will be a handful of games that are an exception, but for most of todays games you will be good.
google graphics card hierarchy and see which one does the best at your price range...bingo!