single purpose zwave range extenders
Zwave range extenders were helpful for the first few generations of zwave because many individual devices aimed for minimal power use, and so had pretty weak transmissions. But by the fifth generation (“z wave plus”) Power management had improved significantly and pretty much all z wave devices transmit at maximum allowed strength, so the single purpose zwave “range extenders“ don’t do any more than any other Z wave repeater, so you usually get better value out of just a plug-in smart plug or a light switch. 
There is one exception, and that’s the ring z wave extender, but it’s not because you get more distance from it. It’s because it can switch to battery power when the Mains power is out. This is really important for zwave based security systems because it means that the battery powered sensors will still have an active repeater to help them get back to the hub, assuming the hub has a secondary power source (which most smartthings/Aeotec hubs, do not).
So the Ring range extender is a great device for a security system using a different Z wave hub, but it doesn’t really serve much purpose in a smartthings setup unless you have your hub on a backup UPS for operation during power outages. Otherwise, a dual purpose repeater will do just as much as far as covering additional distance, and likely be a better dollar value.
As far as what edge, driver to use, as long as it joins your network, even if just as a “Zwave thing“ it will perform its repeating function.
Reaching a distant sensor
So that’s part one of the discussion. Now onto your specific use case.
It’s not surprising that you can reach the sensor in the garage and not reach the one on the outdoor shed, even though the one in the garage is physically somewhat closer. Reaching a device isn’t just about distance. Assuming the garage is an attached garage, signal will be able to go through an interior wall, and that’s typically much easier than going through an exterior wall or door, which are generally thicker and with insulation.
And then there are weather conditions, in particular humidity. For some complicated technical reasons, zwave just isn’t great at getting through high humidity due to some dispersion issues in the algorithm. There’s nothing you can do about that problem itself. But it’s the reason that so far there are very few outdoor zwave Sensors. (This will change with zwave 800, but we aren’t there yet.)
But there are definitely zwave models that have better range than others.
So next we need to know the specific brand and model of the sensor You are trying to reach. The easiest way to improve range in Z wave is to get newer technology. Zwave plus has better range than Z wave classic. Zwave 700 has better range than Z wave plus.
It might be that all you need is to switch to one of the new Zooz Z wave 700 sensors.
Zooz Z-Wave Plus 700 Series XS Open | Close Sensor ZSE41 - The Smartest House
location, location, location
You can use just about any Z wave mains power device as the repeater. The key may be finding the best position for it. 
I often find that a light switch one floor up from ground level near a clear glass window is the easiest way to get Z wave signal to an outbuilding as you can get up above the tree line. (Trees contain a lot of water, water blocks signal.)
(I used to often use Z wave lightbulbs as repeaters for some of these situations, but they are getting really hard to find these days.)
a WiFi alternative
Or you could skip zwave altogether for this particular location and use a Shelly Wi-Fi sensor. That will have 2 to 3 times the range of even the Z wave 700 devices. (although most Wi-Fi devices have terrible battery life, Shelly is the exception. They have worked very hard on power management and their battery powered sensors do seem to achieve 12 to 18 months, battery life, which is impressive. Be prepared for bigger devices with bigger batteries to do this, though.)
https://www.shelly.cloud/en-us/products/shop/shelly-door-window-2
There is a manufacturer-provided integration with Shelly through the smartthings app, or a community-created edge Driver.
summary
So… I think the ring zwave range extender is an excellent device for some very specific use cases, but it doesn’t sound like those are the use cases you are trying to solve. otherwise, I don’t generally recommend the single purpose “range extenders” for zwave. They don’t do any more for the strength of your network than any other Z wave repeater, so you might as well get one that serves another purpose as well, like a smart plug or light switch.
In your particular case, I would first look at the exact brand/model of the Sensor you are using. Maybe you can get a newer Z wave generation, and improve distance coverage that way.
Also, I would look at placement of the repeater.
Or maybe a Shelly would make more sense. That would give you a lot more range to play with, and no repeaters needed.
@jkp
