There are several diffrent programs that can do what you want. There is no one best solution as they all have thier advantages and disadvantages.
To answer your first question, copy guard, there are three main programs to deal with it, anydvd, dvd decryptor and smart ripper. This is of course not everything needed to copy, but this is the first stage where you remove copy protection. Dvd decryptor and smart ripper are both free and rip (copy) the dvd to your hard drive. A folder on your hard drive basically becomes the equivalent of the dvd. In the process they remove the copy guard. Any dvd is not free but does not require it to be ripped to the hard drive (it runs in the background and disables the copy guard). You can copy directly from a dvd to a blank dvd with anydvd (most programs are still going to copy to the hard drive but it is not an extra program/step for you to have to worry about). You can use diffrent combinations of these programs. For instance (someone corect me if I am wrong here), you could have anydvd running in the background and use dvdshrink (skipping dvd decryptor because you are using anydvd). If it is taking you 50 minutes to rip using dvd decryptor it is probably your drives fault. I gather that you are using the maddog only (you don't have a seperate dvd-rom for reading). There are two main options to improve this. Your drive limits how fast you can read a dvd-9. This is very possibly the manufactures way of trying to prevent you from copying movies. It doesn't stop you but it slows the process down to frustrate you (I guess that they hope you will give up). You can either used hacked firmware that removes the riplock (you are going to want to update your firmware anyway so check into this). Go to the recording hardware forum and then to the nec forum (your mad dog should be an nec3500). You can find info on firmware there. The other option is to get a high speed dvd-rom and use it to read. You can get one for not much more than 30$. Here is a thread that talks about two of them
I am assuming that you are wanting to backup purchased movies. It will therefor often be the case that you will have to compress the movie to get it to fit on a single layer dvd blank (because dual layer blanks are still way to expensive). clone dvd, dvd shrink, nero etc. all perform the same function here. You do not need all these programs, you only need one. dvd shrink seems to be the most popular free one. I prefer nero. If you have nero ver 6.??? then you can get free updates. With the exception of copy guard nero 6.??? can do the entire process from start to finish. Try dvd shrink (after all, its free) and nero if you have a new enough ver and see which you like. You can try clone dvd and others if you like but since they cost money, you might as well try what you have and or what is free.
If that confused you, use one of these programs (any dvd, dvd decryptor, smart ripper) and one of these (nero, dvd shrink, clonedvd etc). You can use any one program from the first group with any one program from the second group.
I personally highly recomend anydvd and nero.
Here is a guide for nero
It is very easy to use. If you just want to make an exact copy, you can skip steps 5 and 6 in this guide (they tell you how to remove content) except for the las step in 6 which is just clicking next.