The simplest PC solution is to buy a TV card (preferably one with composite or s-video inputs). Most VCRs have audio out (left and right) and video out sockets, which you would connect the video out to the tv card (standard phono lead normally or phone to s-video lead), and the audio out to the pc's sound card (you may need a 2 phono to 3.5mm jack lead).
Most TV cards will come with basic recording software, but these are usually limited and only produce file suitable for a PC.
To produce DVDs, it is normally best to use a commercial package such as Cyberlink's Powerproducer which is quite cheap and easy to use and has modest editing capability. This is a good package for beginners but there are many other similar packages ranging from simple to very sophisticated.
Improving sound quality is probably for real experts. By and large, recordings cannot be better than a source recording unless you apply advanced techniques which would normally be very expensive.
The same is also true of video pictures. However, recording to a PC (or stand-alone picture) can apparently eliminate some of the hiss sometimes see in a video recording and give the illusion of an improved picture (actually the recorded picture is usally slightly softer - basically the same technique that make Hollywood stars look younger!).
For hard disk storage the answer is lots (say 160MB or more)! It is a good idea to have a second hard-disk for the recordings as DVD video editing works the disks very hard, and thus keeping it on second disk minimises the risk of a disk failure of you main operating system disk.
Another solution is to buy a stand-alone DVD recorder which you simply connect to the VCR. However, most stand-alone recorders will not copy macrovsion protected video tapes though. The Liteon DVD recorders can be hacked to bypass this (sse liteon forum for more details).
Finally, why bother with protection? It is very expensive and only realistic for commercial enterprises.