DVDShrink is rather outdated as a decryption/ripping program, and it will not be able to handle any dvd that has extra copy protection added other than plain CSS. Many different types of structural protection schemes have been released since development stopped on DVDShrink. Shrink is still a good transcoder, though that method of compression is inherently worse than using a full encoder for reducing the size of a dvd.
A dvd (with no extra protection) that is copied by Shrink should be playable on any dvd player. Problems sometimes happen when you use poor media, or burn too fast for a particular type of disk, or you just have a picky player.
As a replacement decryption/ripping program, I suggest getting DVDFab HD Decrypter. It is the free section within DVDFab and will continue to function even after the trial for the main part of Fab expires. You can find it here: http://www.dvdfab.com/free.htm
You can rip the dvd straight to the hard drive as files and play them back using any number of software programs. Some are free, like VLC media player and Media Player Classic HomeCinema. And there are commercial products like PowerDVD and WinDVD.
You don’t have to use compression to rip to the hard drive. DVDFab HD Decrypter won’t compress. Even with Shrink, you can set it to no compression when ripping. This gives you the entire movie, with no degradation of the video whatsoever. The only downside to doing this is the size of the files. An average commercial dvd will be 6gb or more, including extras. You can choose to rip only the main movie, but you lose menus, commentary and extras that way.
Many people choose to rip and convert to a different format when storing movies on the hard drive. The only good reasons for doing this are saving space and having a compatible format for streaming with certain devices. Any time you convert to a different format, or compress, you will effect the quality of the video adversely. If it is done well, you probably won’t notice this slight degradation of quality.
Conversion also takes quite a lot of time. If you are interested, look into programs like Handbrake, MeGui or AutoGK. Many people still use xvid codec in an avi container, especially since they can burn those files to a disk and play on compatible dvd players, but the more advanced users have moved on to H264 in mkv or mp4 files when storing on hard drives.