Yes and NO.
Anytime you compress anything you always loose quality.
When you compress a Video or Audio file it quite simply throws away pieces to make the file smaller. Some encoders do better than others but for the most part the difference will be hard to see. The idea is to throw out pieces the human eye can not detect or the human ear can not hear when compared to the original.
However, you will start noticing a degradation in quality if you start to compress too much. Some encoders just do not do thier job well and its always noticable.
Alot will depend on what you want to do with the file. But in general, x264 for video is a very good choice.
What bit rates to use so that it looks as good as the original will depend on the resolution you are working with.
AS mentioned I highly recommend x264.
There are 2 main GUIs for this codec. Handbrake and MeGUI.
In my humble opinion, MeGUI is the superior of the two but it comes at a price. Longer Encoding times and a very steep learning curve,
Handbrake on the other hand has a smaller learning curve and is a bit more straight forward and easier to learn.
Both however, do a excellent job. It just depends how much time you want to put into the projects and learning the ins and outs of the programs.
For reducing and storing you camcorder files, you may want to try a MP4 with AAC audio. This is a good choice as it looks and sounds very good, and is compatable with nearly everything. Even Android and Apple devices.
For encoding to DVD, you are better off using the original file for the conversion.
Also,compressing a file thats already been compressed multiplies the quality loss significantly.
YES, you can use your compressed files to create DVDs, BluRays, compress further, or even convert to another format. However, if the goal is to minimize quality loss aas much as possible, this is not a good idea and the original file is the best option.