Many people will actually give you you their old Hi8 camcorder, if you make high-quality DVDs with menus and covers out of their old Hi8 tapes in return. Decide what kind of cases to use and whether to print the covers in color or black and white. Then, make a clear agreement about who pays for the blank DVDs, cases and printing. Keep the receipts. Finally, do the work properly: clip a bunch of interesting snapshots off of each tape, use the snapshots in the menus and covers, burn the DVDs, print the covers and insert them into the cases. Return their Hi8 tapes to them.
For reference, the commercial price of converting a video tape to a DVD with a color cover that includes snapshots is about $15 per tape, see for example, The Photo Archival Company. For 10 tapes you are providing a service worth more than $100 in exchange for an old camcorder that's no longer used.
Note that a used Hi8 analog camcorder which originally sold for $899 will record better video and sound than a new $249 miniDV camcorder. At this point in time, however, it is difficult to recommend a Hi8 camcorder based on quality considerations. The main reason to use Hi8 is price. If you don't know anyone willing to give away their old Hi8 camcorder, then a miniDV camcorder will work just fine and they are anyway more convenient in size.
If you must make a choice between spending money on the computer or on the camcorder spend it on the camcorder. Get a camcorder with optical image stabilization. The video you shoot today will be irreplacable after your children grow up. The better it is, the more you can do with it later. If possible, shoot your source with an HDV camcorder. There is no need to buy an expensive computer to edit HDV and master a DVD. Let the camera down-convert HDV to DV as you export it and then use your old computer for editing. Keep the HDV source tapes and remaster them on a new computer after high-definition players become popular.
Stick with tape based camcorders as tapes can be stored and have a longer shelf life than disks. Never reuse a tape. Never use the LP mode of miniDV tapes. Always rewind your tapes. Store them in a cool dry place. Home videos get more and more interesting the older they get. Stay away from hard-disk camcorders and flash camcorders. Only a genius would be able to archive the video shot on these kinds of camcorders over long periods of time.
If open-source tools for authoring and playing back Matroska files with menus become widely available, then the right way to archive home video may be as Matroska files. If these files are made using the h264 video and ac3 audio streams described in H264 HD Video Workflow, then they could be remultiplexed and mastered to HD-DVD or Blu-ray disks whenever desired without reencoding.
Media players such as the Popcorn Hour look like a nice way of organizing home video for playback on the television. As I don't own one of these players, I can't comment on the best video file format to use. I've heard that Matroska is supported; however, I don't know if menus are supported.
If you are rich and and saved money by using the free software and techniques described here, please consider contributing the money you saved to a good charity. If you are poor and couldn't afford the proprietary software solution in the first place, then please enjoy making your videos anyway. Bring light and happiness into the world with your videos.