If your footage is truly analog (for example VHS, 8mm, hi8, then I would obtain (or borrow) a working DV cam (Sony DV 8mm, etc), dub the analog footage to the DV cam. Next, you need a PC or laptop with a firewire "in" port (good luck finding such a laptop. I have never had success.). Back in the Windows XP days, many quality PC's included one or more firewire ports. Today those ports have been replaced by USB for which, to my knowledge, there exists no capable software or digitizing devices to make quality DV to analog conversions. I have several old XP computers with firewire ports, so I capture the DV footage to one of those computers, then transfer the converted footage to my laptop or external drive for editing with Vegas or another NLE of your choice. Vegas in its earlier years had a capture utility called Vidcap. I don't know if the new versions still have it or some other utility. I use a free program called scenalizer or scenalizer live which you can download and use to capture DV footage. It works reliably.
There are plenty of USB conversion products out there that will take analog footage directly to your PC or laptop via a USB connection, but I find that the quality that those products deliver is so inferior that I refuse to work with it. You mention tht you are not looking for a pro-level device, so, if you would be content with digitalized footage that is of lower quality than your existing analog footage, these may work for you and be less hassle than the process I described previously, but, IMO, once you get the necessary pieces (DV cam which you may already own, PC with firewire ports which you may also already own), the only hassle is the time it takes to dub from analog to DV tape, then capture using Vidcap or Scenalizer. All of this dubbing and capturing involves starting the process, then coming back occasionally to check on the process so that you can stop the capture when completed. I do not find it all that cumbersome, and the final product is the best copy of your analog footage that you can achieve. I doubt that a professional house could deliver better. It takes a little time, but, for me it is worth it. If my laptop would accept a firewire card, port, whatever, I would purchase and install one in an instant. I really don't get why USB supplanted firewire which, IMO, has always seemed faster and more robust right from the get-go. It did not have to go through three iterations to achieve optimum through-put. I am no expert on these matters, but have been an avid amateur consumer of video cams and editing software since before Sonic Foundry introduced the first versions of Vegas. I currently use Vegas Pro 16 and an open source program called Blender (runs natively in Linux) to do my editing. I have most of the Sonic Foundry versions of Vegas, most of the Sony versions, and, now, a couple of the versions introduced by Magix. Vegas isn't free, but, IMO, it is one of represents one of the most powerful editing choices available, and the interface has always been more straight forward and fast to use than any other NLE with which I have worked.
Good luck with your conversion(s). Try my suggestions. I think you will be pleased.
Assuming your existing camcorder does not have FireWire, find an old Canon ZR at goodwill to do the a/d passthrough. Much better than novelty USB converters, as are the Canopus ADVC300 and set-top DVD recorders, which is what I use now.
Thank you all for the tips. I was considering using an old Canon XL1 DV camcorrder or Sony VX1000 to do exactly that, but I was concerned that it would only give me DV-quality video. On reflection, DV is probably better than the original Hi8, anyway. I might be being too picky. About the 1394 connection: I just recently bought a cheap Firewire card from Amazon and put it in a new Dell machine. It works fine bringing DV footage into Vegas. So I'll look into the pass-through capabilities of my DV cams. What a bitter irony it is to have to spend so much time preserving my personal memories from the advance of technology.
Another choice is to use the S-Video output of your Hi-8 camcorder. I use card similar to the Hauppauge WinTV-HVR-1265 for $50 US. It is a PCIe card that will take the S-Video signal and record it to digital. S-Video is better quality than Composite. Of course it is not as good as using a pure digital signal.