I cant get the newegg links to work . My problem not yours ....
a 5770 can game reasonably with a 1900 x 1080 resolution .
Some games you will be turning detail down to keep the frame rates up
If you are going with a 22 inch monitor then a 1650 x 1050 will give higher frame rates and very decent quality image . Id only buy a 1080p 22 inch monitor if watching hi def movies was important to you .
The size of the monitor is not important . Only the resolution.
Buy whichever fits your budget and has good reviews
My connection speed over 3g is too slow for newegg still
but the sapphire on Tiger direct has the reference cooler . If the MSI is the same its actually an identical card and just has either saphire or msi stickers on it .
You buy the cheapest one , or the one with the best game since the quality is identical
Later they changed to a more open style fan and it runs cooler and quieter . Get one of those if you can