One option to convert from VHS to digital uses a digital video camera as an intermediate device. It is required that the digital video camera permit appropriate input, either S-Video and audio or RCA type video signal separation, (left, right, video). It is also required that the camera have a direct feed to the computer. My way-old Sony digital camcorder (Hi-8mm format) has a USB connection that does not have the bandwidth to provide suitable connection but does have a Firewire™ data port. My computer has also this data port.
The VHS device would output to the digital camcorder, convert it to digital and pass it through the Firewire™ connection to the PC. The computer would have to have appropriate software to capture/record the video from the camera.
It is not difficult to find an inexpensive digital camera via craigslist or eBay and I cannot address today's technology in that aspect, but it's not as likely to contain such "old-time" connectivity.
For the software aspect, if you don't spend the big bucks on a brand name package, one could use a Linux machine running Kdenlive or one of many other options. I've used Kdenlive and found it to be intuitive and responsive on a Linux machine, somewhat buggy and crash-prone in the Windows version.
A quick check on eBay shows my old camera, dcr-tv350 running between one and two hundred dollars.
There are also devices which are a VHS tape player on one side and a DVD recorder on the other. The manuals are complex unless you are aiming for a straight dump from one medium to the other. Another quick search shows they are far more expensive than a used camera in the middle.