Personally, I have tried weed fabric/landscape fabric and I now have a seething hatred of the stuff. YMMV. As the wood chips (or whatever is on top of it) break down, weeds start to germinate above the fabric, while the fabric interferes with normal processes in the soil. I consider it worse than useless in the long term.
Given the age of your garden, I'd suggest just adding woodchips (or newspapers under woodchips) to what you have (not going to the effort of digging out right now), and running a lawnmower over them if your paths are wide enough for a lawnmower, or a hoe through them if not, because I'd bet you have not arrived at your final path/bed layout yet - voice of experience...
When you are sure you've arrived at a long-term layout, if woodchips are easily available to you, a simple 4-6 inches of them makes a pretty weed-free (and easily weeded, if need be) path that can be maintained by adding an inch or so of fresh chips yearly, and which does not have an annoying plastic layer lurking under the surface. I'm unclear how Bamboo finds them a potential trip hazard, for anything I'd call chips, rather than chunks. I find that they make a nice smooth path, and you can roll them if you like. The best way to keep the chips on the path is to keep the path lower than the beds - and little chip migration at bed edges is not a problem.
Other approaches include turf (do size for a lawnmower, and consider edging (the process) if that's not something you consider by default - virtually all the British gardens I've visited edge/trim turf edges, it seems a far less popular concept in the US), thyme-turf and chamomile-turf, stone slabs with thyme in the joints, concrete, etc. - in my garden, the introduced european fire ants make hard surfaces a dubious proposition, as they like to set up housekeeping under them (and are both very annoying and hard to kill.)