Wow, that is one shiny jack...
As for mounting it, I am opposed to inside the Jeep personally. PIA getting it out, especially if you have a hardtop. A 48" hilift will actually just sit right in the back of your Jeep between the rollbar and the tub, essentially where the picture shows it, but 8inches lower. Of course, if you roll over, you'd rather not have that loose inside. I ended up getting a swingout bumper that holds my tire, jack, etc, but at one time I was going to check around for wheel studs that fit in the jack frame holes. My plan was to weld wheel studs to the stock bumper to hold the jack. It also would give me the option of having a locking wheel nut to thwart unmotivated thieves.
There is also a company that makes a jack mount that fits on your hood hinges. Looks cool, but I just know that is a big dent and loss of paint waiting to happen when you go to remove or replace the jack.