I'll get some similar tests up with the 7290 and a 7290A as a comparison, but I can speak a bit to analog capture on modern hardware - I've been capturing a number of sources for live streaming and recording and have tried a few options.
For hardware, something like what you've got seems to be the easiest to work with. There are cheaper dongles marked "Easycap" or similar (the brands are fairly fluid, they're usually just rebadges of a handful of products, though I think ezcap is either a maker or a primary brand name) which interface fine but have lower image quality, but the one you mention by Ezcap (not the same) and UCEC and others seem to be better laid out and give somewhat better noise performance (not a huge difference, but better). On the "high end" of these capture dongles is the elgato video capture units, which are quite a bit more expensive, but which offer at least as good capture as the Ezcap/UCEC units, maybe better, and everything's got its own quirks.
If possible, look for a capture device that supports UVC. The USB video standard ensures that it's recognized by lots of software and that the software has some control over its resolution and other features, and the way it plays with software is the usual main concern. The more rectangular Easycap dongles (and other brands) will work fine and support UVC, but have the lower video quality, but the only reason I can see for going beyond a UVC Ezcap/UCEC unit is that they don't seem to play nice when there are multiple on a single system. That means if you want to record multiple sources, you can go back to the lower video quality units, or shell out for the elgato units - which are not UVC and while they work great, there will be some software (microsoft's camera app, discord video chat, others) that doesn't support them.
On the software side, if your input device is UVC, the default camera app works in windows but limits the settings you can access most of the time (I'm sure there are equivalents for other operating systems). Manufacturer specific recording apps often work but lack features or are tailored entirely around recording so they have a set autoshutoff or extra buffering or other "features" that make them ill suited to live work. My favorite program, and what's been most versatile so far, is OBS studio, a program designed for livestreaming. It takes more setup to use than most (have to setup a scene, a source, arrange them on the canvas), but it also will take multiple (even varied) input sources, gives you access to the hardware settings they offer, and allows easy application for text or graphic overlays, scene transitions, and similar - meaning you can avoid the need for anything more than transcoding after you've captured. It is worth mentioning that the elgato capture cards only seem to support the widescreen SD output resolutions for some reason, so especially in OBS the image can appear stretched on default settings, but the software also allows you to manually transform the captured image so you can get to 4:3 or 5:4 as needed for your source. Virtualdub will generally capture well, but I find the setup process for streaming capture devices more tedious and have run into issues with non DirectShow capture.
There are also a number of PCI and PCIe based capture devices that are supposed to be what people doing this professionally have used (not sure if that statement is current), but I have no experience using them (small form factor PCs don't have slots to spare!)