So much is dependent upon your budget. What style of wedding video do you intend to produce? There are three styles - Documentary, Journalistic and Stylistic. Of course, you could get picky and break things down to dozens of styles, but these are the basics.
It's a great idea to work for an established videographer for awhile before going it alone. Stylistic videographers can often get by with a single camera and wireless set, if it's a simple ceremony with only the officiant and couple speaking and no music or singing, etc. - IF the officiant will be very close to the couple at all times when he is speaking. In my experience, this accounts for a small percentage of ceremonies where videographers are hired.
If the ceremony has more activities or if you're doing journalistic style, etc., you'll really need more cameras and more microphones. And I'm just begining to touch the surface on gear. Our first DVD in our wedding videography course is mostly spent on this topic. Being practical and realizing that most of us work on a budget - especially when just starting out, we break things down into levels of what you really need to just get started, and the priorities for adding more gear, etc.
A digital recorder can be a great asset, but I notice you said "digital voice recorder". These are generally lesser quality than a professional digital recorder and usually only offer mp3 file types. While mp3 might be alright for most voice situations, the problem is that we often must do some sort of work on an audio file and when you edit a compressed audio (or video) file, the quality drops quickly and noticably.
In short though, we use digital recorders in a variety of ways. If I have a singer and violinist (for instance) performing next to each other, I may mic both and connect into the DR, eliminating the need to mess with radio gear and freeing up two camera inputs.
Or, in a free-wheeling reception where a handheld mic is being passed around for toasts, etc., we'll tap directly into the DJ sound system.