I am not familiar with the Oregon 600, so I looked it up.
https://www.garmin.com/en-US/p/113532

It looks like it uses the same type of handlebar mount that my Garmin 62S or 64 use. The genuine Garmin mount is a bit tight, the cheap aftermarket ones a little too loose. I use both, have different ones on different bikes. My previous comment on a tether still applies. The mount is attached to the handlebar with zip ties. I found that wrapping a piece of rubber from an innertube around the handlebar before installing the mount on top of that helps keep the mount tighter on the bar, less likely to rotate around the bar when you hit bumps because the mount and the zip ties are less likely to slide on rubber than on metal. The genuine Garmin mounts are cheap enough that I would suggest that instead of aftermarket, I think they used to cost a lot more.
https://www.garmin.com/en-US/p/11411

My GPS units are not touch screen, I have no comment on that topic.

Uses a mini, not micro USB cable to plug into computer. Those are getting harder to find.

It says it uses AA batteries or can use the Garmin proprietary battery pack.
https://www.amazon.com/Garmin-Rechar...dp/B00B1QUF8O/
That battery pack is simply two AA NiMH rechargeable batteries held together. When that battery pack is installed in the GPS, it presses down a button that tells teh GPS that that battery pack is installed, and then you can charge the battery with the mini USB cable while riding from a powerbank if you want to.

I use regular NiMH AA rechargeable batteries (Ikea 2450ma Ladda) in mine, and I have a small piece of sheet steel I cut from the top of a soup can taped on top of the button, so AA batteries push on that metal piece that pushes down on the button. Thus, I can charge the batteries while riding. But I do bike touring where being able to charge while riding is convenient. If you are using it for day rides, you can just start out with freshly charged batteries every day instead. I also use Eneloop AA rechargeable NiMH batteries in mine when the Ladda batteries are not handy at home. If you prefer disposable batteries, that is your choice, it works on them too.

If you add maps to it, you might want to put a 32gb Micro SD memory card in it if it does not already have one. I think Garmin sells their maps on memory cards like that to, but I am not sure, last time I bought Garmin maps was over a decade ago and they were on CDs.

If you get it, I suggest you set the screen so it does not time out, keep displaying. And I suggest you only use backlight when needed. When I say that, I assume yours (with touchscreen) is like mine (not touchscreen) and they work great in direct sunlight but when the sun is low, then back light is needed. I find that keeping my screen on does not reduce the battery life much at all, but the backlight really cuts the battery life, so backlight should be limited to when needed.

Make sure you get as many of the extras as you can if you buy it, the Mini USB cable (if he has one), etc.

You mentioned backpacking, I have a small generic nylon zipper bag strapped to one of my backpack shoulder straps to hold my GPS and my camera, but mine is not touch screen, I have no idea how a touchscreen behaves if the GPS is in a pocket, etc.