Well most of the 22-24" screens are 1080p nowadays, excluding some 16:10 24 inch screens like the U2412M, which have res of 1920x1200 but usually these are more expensive and harder to find.
Considering this, the 550Ti will play most games at high settings @ 1080p, some on mixed med-high settings but will struggle with newer games with AA/AF enabled, so you will play games without AA/AF enabled, same goes for 1200p.