You can burn home movies in VideoCD format (or VCD) and your DVD player will probably play them. If it can play CD-R's, then in all likelyhood it will play VCDs.
In order to get the videotapes into your computer, you need a video capture card or a video card that can also do capture. I currently have an ATI All-In-Wonder 128 Pro card that I use to do video capture from both tapes and from the built in TV tuner. The quality of VCDs is not as good as DVD, but it will do for home movies. You may need a fairly powerful PC in order to do decent video captures depending on the type of card that you purchase.
If you have any specific questions, please PM me and I'll try to answer them.