The series is basically a case-of-the-week procedural, with the team having to find and then get rid of a particular demon. There is also a serial arc that is tied to Constantine's past that we get a few hints about, but the series was canceled before it could be fleshed out. Of course, most fans of the show know that the character was brought into the Arrowverse when the character appeared on the series Arrow and then became a regular on Legends of Tomorrow. I think the series would have been a lot better off being on The CW as it could have crossed over with the other Arrowverse shows from the get-go, but it was probably too close to the series Supernatural which was, at that time, The CW's longest running show. But, the series was just too dark to get enough of a fan base on a regular broadcast network and was never going to get the kind of ratings it needed to be renewed.
For those who get the blu-ray set, the series looks and sounds great in HD. The one benefit of being on a major network is that it got a huge budget so the special effects looked movie quality. As far as extras go, there are a couple of very short behind-the-scenes featurettes, a trailer for the series, and two Comic-Con features. One is a portion of the Constantine panel (that runs about 11 minutes) and the other is the DC Comics Night at Comic-Con 2014 Presenting Gotham, The Flash, Constantine, and Arrow, which runs just under a half hour.
Overall, the series is good, but was probably doomed from the start. The showrunners made the curious choice to abandon a major character from the pilot who was clearly going to be a series regular and basically swapped her out with the character of Zed. As I said above, it was probably too dark a show to get traction on any of the major networks as it was only going to appeal to comic book fans and they alone cannot generate the kind of ratings needed to keep a series on a major broadcast network. And, given the themes of demons and the occult that occurred in every episode, there was no chance that casual viewers were going to stick with the show. So, if you watch the show, just know that the series has a pretty unsatisfying end and while the character of Constantine lived on in the Arrowverse, the plot lines (and other characters) from the series did not.