It's a kryptonite u lock. They make a bunch of different ones. this one has the attachment that holds it to your frame.
It all depends on how long you're going to leave your bike locked up for. In any case, I would go no lower than Kryptonite's "Orange" level locks. If I was using that lock that you linked, I would leave it out max for an hour, no longer.
I actually hate the size of the Mini-5 and find it difficult to find a place to lock it to, as it is tough to squeeze in the rear wheel through the rear triangle and a standard street pole most of the times. Instead, I run an Evolution Standard lock: https://www.amazon.com/Kryptonite-Evolution-Standard-Bicycle-FlexFrame/dp/B005YPK99I/ref=sr_1_2?ie=UTF8&qid=1496113700&sr=8-2&keywords=evolution+standard with a cable for light lockups.
In most cases though, I run with a orange level New York Chain, cable and Fagheddaboudit U lock for versatility. If I can't fit the rear wheel and frame with the U lock, I'll use the chain instead (I think the U lock is harder to steal from than the chain) Then I use the other lock for the front wheel and frame.
Kryptonite Evolution Series 4 Standard is big enough for your needs: https://www.amazon.com/Kryptonite-Evolution-Standard-Bicycle-FlexFrame/dp/B005YPK99I/ref=sr_1_3?ie=UTF8&qid=1501758780&sr=8-3&keywords=kryptonite+evolution
I've lived in the city for 4 years. Had 5 bikes in the time I've lived here (1 exploded (carbon fiber), 1 got run over, and the other 3 are in great condition) I use divvy probably once or twice a week in conjunction with my other bikes. I live by Lake and Western and bike to the loop every day on one of my personal bikes - I'll usually grab a divvy when I go out for lunch during the week or on the weekends to grab an extra bag of chips or some beers if I'm at a party or something.
I have both and love the flexibility of both. I've never had a bike ripped off (completely or for parts) save for a quick release bike computer that I left on my handlebars outside a bar on a friday right after work.
I use a big ol kryptonite U lock and either a cable through the front wheel or the Sheldon Brown method