The easiest and cheapest answer is a DVD recorder. Panasonic, Pioneer, and Philips make decks to record DVDR disks directly from video input. Then you can do simple editing and add menus. What they're no designed to do is make more than one copy. It can be an authoring solution, and later use a computer with a compatible DVD burner to make copies.
The expensive, but more flexible and professional solution is to build a computer-based video editing system. With the Betacam, you'd need an analog capture card. Then you'll need a dedicated hard drive to store your video files. After you edit your video, you'll need to transcode the video to a DVD compliant format. Then you'll need to use DVD authoring software to design the DVD structure and generate the DVD files to burn onto your DVD.
I personally use a Matrox RT.X100-based PC to capture DV and analog video in Adobe Premiere. I then take the edited project and export it in realtime to DVD format mpeg. Next, I use DVDit PE to author the DVD and a Pioneer A03 to burn the DVD. This solution allows me to easily create multiple copies for resale.
I'm sure the VideoGuys will be happy to discuss possible solutions with you.