Serious issues would be if DVD Player crashes or reports an error during playback, which does happen occasionally with rips. If you can start playing it and fast forward though it successfully, then the MTR rip has been successful.
As far as Toast, if you are in the VIDEO_TS folders tab then just dragging the main folder into the window as you have described is correct- then it is just a matter of whether the VIDEO_TS folder included has valid data.
The automatic opening you described is easy to take care of-- just do into your System Preferences and click the "CDs & /DVDs" pane and you can define what you want the system to do with both types of disks when they are inserted. I just have everything except blank CDs set to "Ignore" for simplicity. It used to drive me nuts that everytime I inserted a movie I wanted to rip it automatically opened DVD Player and started playing it, so I know what you are going through!
I personally have never tried Wondershare myself since I have not had problems with MTR through the years, but maybe someone has and can share the info.