I think you have two possibilities:
1) buy some video grabbing device for your computer (various types - external for usb, internal for pci slots etc.), connect it to the computer and record the video to the computer (recommended is MPEG2 format) - it will take the footage real duration to record it. Then you can use something like Avidemux (free and opensource, you can work in Copy mode, so you do not need to re-compress the video) to cut bad parts or to split the video into small parts.
Finally, you can burn this as DVD-video, but if your players support MPEG-4, then I would use it. MPEG-4 ASP (XVID), 1500 Kbps video bitrate with 128 Kbps CBR stereo MP3 sound, AVI container is approved format, which worked on many standalone DVD players with DIVX support and also on many current LCD TVs with usb input.
2) record the video using your DVD recorder, then transfer the video from DVDs to your computer and use the same technique as in 1). This approach does not need to buy any new device, but you will have a plenty of DVDs with your raw video (maybe you could use RW disc to avoid this).
I chose MPEG-4 AVI instead of MPEG-2 as output format because there is no visible quality loss but significantly smaller filesize so you can put hours of your video on one DVD disc.