You'll have to resort to an unofficial (or semi-official but third-party-dependent) solution to get the Ring device integrated, if it even can. There are a few options, but I'm not sure if any support the Ring Smart Light you linked to. These could include IFTTT applets, an Alexa or GH routine, or the community-developed Ring integration app--but again, you'll have to check that this particular device works. In any case, there is no 100% native Hubitat integration.
The Hue device would certainly work, though it may be a bit expensive for that sole purpose. Hubitat comes with a native, local Hue Bridge integration (and there are at least two community-created options).
I'm not sure what other products there might be in the battery-powered arena--that tends to make things difficult, both from a "must be always listening" perspective and the fact that generating the light may also drain battery. There are pseudo-portable mains-powered solutions you could use like an RGB LED controller and lightstrip (basically a DIY Hue Lightstrip, but you can make it a short length; there are lots of 12V and 24V options and even a few 5V USB options that might be more suited for this...and for that matter, I guess even the Hue Lightstrip would work, but if you don't need it then it's about the same price as the Go that actually matches your desired features). That's something I once thought of doing on my own but haven't convinced myself it would actually be useful enough to do yet. 