I also have a Sony digital cam (pics only, no videos)
What resolution are you using? Sony (or another source) reccomends 640x480 for posting on the Web (same as you did with the "Vette) as a balance between quality of image and minimum bandwidth usage.
However, when you print a 640x480 sized image (especially if you print 8"x10"), it looks pretty grainy.
So, take your pics at the highest resolution you can (mine does 1200x960 or thereabouts). You can always reduce the resolution using Irfanview or another image editor for posting purposes (save the reduced resolution as another filename!!! Otherwise, you overwrite your original, higher quality image.)
The other thing is the paper and printer you're using. You really need to use a quality photo paper (HP makes some nice stuff...a bit expensive...around $30 for 25 sheets). Also, your printer must be capable of printing high resolution pictures. We have an HP 952C which does a fine job (using HP glossy or matte photo paper).
Another alternative is sending the pics to an online photo printer (we've used <A target="_blank" HREF=http://www.shutterfly.com/index.jsp>this one</A> with great success.
Now, you're using a video camera. I don't know if you can adjust the resolution of the stills, especially if they are "captured" from a video. As the "frames" in a video move so fast, quality of a frame (image) isn't as important. Your eyes can't "read" an image in a video, so your brain fills in the image based upon the rest of the scene. You're going to have to read your manual to determine the best "quality" for the vidcaps.
But, the quality (resolution) of the original picture file is what determines the quality of the printed picture.