If you don't have the option to put it indoors, then your garage closet can work...but, be sure to bolt it down to the floor and to wall studs, and use a dehumidifier. Unless your garage closet is ducted from the house heating and cooling system (doubtful) then there will be more temperature swings than occur inside your home.
As for the safe itself...there are much better safes on the market, but they also cost a lot more. Generally speaking, you do get what you pay for...this model may be easily pried open or cut into with hand/power tools (which you may be providing in your garage.) A home alarm system doesn't usually include the garage, so a thief may have more time than he would inside the home...but on the other hand, a thief may not spend much time looking in the garage anyway, unless they are specifically looking for garage items (tools, etc.)
Another thing you could consider is, once you install the safe in your garage closet, consider putting a steel or vault type door on the closet...something with multiple deadbolt locking points, and either internal hinges or hinges that are drill and knockout resistant. This will give you two layers of protection for your guns.