If you plan on using CloneDVD with AnyDVD you must always have AnyDVD active for CloneDVD to work. AnyDVD removes the copy protection, that is it's purpose. If you disable it CloneDVD cannot do it's job.
For your first movie I would suggest you try using the top button, copy DVD Titles, this will give you movie only and the best quality if it is a longer movie. When you navigate to the drive the DVD is located, just click on only the Video_Ts folder, then click OK. In the next screen you can check the preserve menu button if you like, you should see a loss of about 2 % though which is minimal.
Make sure you disable your antivirus and any other unnecesarry programs running before you use CloneDVD. If you have another program such as DVD43 that removes copy protection installed on your computer, uninstall that program, it will cause a conflict with AnyDVD, it's like asking two people to do the same job, they both get in each others way and nothing gets done.
I would suggest you read the Help file, it is very informative and you can learn the many features CloneDVD offers. Let us know how you make out.