There's different ways to "remove all the extras" in DVD Shrink; the one that saves the most space is using Reauthor mode and only select the title corresponding to the main movie.
Then you can deselect everything except a single audio track, and whatever subtitle tracks you want (if any).
In the Backup Options you should enable "Perform deep analysis before backup to improve quality" and enable "Compress video with high quality adaptive error compensation". The Sharp (default) may or may not produce the best results, depending on the movie, the compression ratio and your personal taste. I use "Smooth" most of the time.
This should produce the best possible result achievable with DVD Shrink, and usually higher than the 55-65% you mention, but it depends on the length of the movie and the original bitrate used.
Your DVD burner is pretty old, and you are likely to get a better burn with a newer DVD burner.
Using quality media is essential and the two you mention should be good.
Burn your DVD at a reasonable speed such as e.g. 8x. Medium speeds such as 6x, 8x or 12x is usually the safest choice, and maximum speed is risky with everything except the very best batches of the very best media in the most compatible burners.
Welcome to CDFreaks!