DVD Shrink will just strip the copy protection out (you can make an ISO file which can then be processed by other programs). Handbrake will just take the video from an ISO file (you might need to mount it using something like Virtual CloneDrive). It's all very easy (if you use one of Handbrakes presets) - the main time consumed will be waiting on the DVD being decoded and the resulting file being encoded. Whichever way you do it, it's going to take time, though little of your own time.
There may well be a program that does it all for you, but I don't know of one, and it won't be well advertised, as stripping the copyright from a DVD is illegal in many counties (something necessary to convert commercial DVDs to other digital mediums).
One thing to note though, Handbrake won't make an AVI file. AVIs are something of the past really anyway.