Can I monitor my pictures on a computer as I take them?

If you have Lightroom then you are already there (assuming your camera is supported)

http://helpx.adobe.com/lightroom/kb/tethered-camera-support-lightroom-4.html

If you search youtube for "thethered capture" you will finds lots of tutorials.

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D300, SB800, 105/f2.8 VR, 50/f1.8, 70-300 VR, Nikon 16-85, Tamron 17-50
http://www.flickr.com/photos/solfried