If you want to compare monitors, the magic figure to look at is the horizontal refresh rate. Sometimes it's printed on the back, but it's always in the manual if you can find it.
Plain VGA (720x480) starts with a horizontal refresh of 31.5kHz and the larger the number, the higher your maximum resolution will be. Use a calculator like this one if you are aiming for a specific resolution and/or refresh rate.
Using that calculator, 1920x1080@60Hz requires a minimum horizontal refresh of 67.8kHz. So any monitor that can handle that or better will be able to show 1080p@60Hz non-interlaced.
For comparison, I have a really nice 19" Hyundai P910+ that has quite a high horizontal refresh of 108kHz, which means it can do 1760x1320@80Hz. So this can easily do 1920x1080. In fact, according to the calculator, it can do 1080p at up to 97Hz refresh rate.