LCD monitor advice

Submitter here. Just bought a new 19-inch LCD monitor. It's an
"off-brand" monitor purchased from a well-known big-box store. I love
the size and the resolution (1280x1024), but I'm not crazy about the
inherent "fuzziness" in the picture. This is especially true of text.
I've tweaked it every way possible, but I can't get it to look clear.

Is this something I have to live with? Or would buying a better-qualty
LCD yield a sharper image? I guess I'm too used to my laptop, which has
an ultra sharp 1400x1050 packed into just 15 inches.

BTW, I'm using the on-board graphics that came with my brand new
motherboard. Maybe a better video card would help?

Thanks!