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There are seemingly so many possiblities and acronyms that I can't find
what I thought should be an easy answer to this question:

I have a Panasonic camcorder that will record on DVD-R or DVD-RAM. I
want to be able to record my grandkids, put the video into my PC to edit
out unwanted material, then combine what I do want and burn it to a DVD
that can be played on any given consumer DVD player hooked to a TV.

What software (I presume I need no additional hardware) will perform
this function for me?

As an aside, I've had previous poor experience with both Roxio and Nero
and have low confidence in those brands.

Thanks for any clarification you can provide.