For most any GPU you are going to need a good high end card and Crossfire or SLI unless you want to game at single digit numbers some what like a slide show. Gaming at 5760x1080 will task most single cards beyond there limits. And even for the single cards that can do it they are going to cost way way more than $250. Low power/low price 3 monitor gaming just does not compute.
For a setup like that you have to spend a lot more money or just not even consider it. It is not for the low budget gaming sorry but that is just the way it is. Pushing that many pixels puts alot of strain on the Graphics system and there is really no way around it. I tried it with just a single GTX 670 when I setup my i5 system last January because my second GTX...