Thanks Sahara. And thank you Army for the info on the eye-bolts and can holders. I'm going to head out to the Depot and get the bolts today and research a little more on the water jugs and spare. Maybe for aesthetic purposes I'll mount the tire on the inside of the box for now; however, that more than likely won't last long due to the already limited space inside. I will also need to fab a little storage box to hold tools and whatnot and that I will more than likely be placed inside as well.
I just mounted an ammo can on my trailer's tongue to hold a spare hub, bearings, lug nuts, paperwork, and misc. trailer stuff; you could really mount one anywhere you have a flat surface on your trailer. Or like you said keep inside so you can remove it when you want.
As far as mounting the spare tire, how about mounting it on the front like I did (pictures in posts above), but rest the tire on the lip of the trailer frame, and get two long 1/2" bolts & fender washers, drill two holes through your boards (one above and one below) to line up with two opposing bolt-holes on the rim, and bolt the tire up flush against the outside front of your trailer's box? If you ever get larger wheels and tires the holes would be easy enough to plug (1/2" diameter wooden dowel cut 3/4" long & tapped in and then stained/varnished over).
Or you could get an 8"x2" board scrap and cut it square (7.5" x 7.5") to use as a spacer between the wheel and the trailer box if you wanted to move the spare out so the tire rested on the trailer tongue if you wanted some space between the tire and box (if having it flush would cause interference with your lid project or securing a tarp around the perimeter).
Or since you've just got the 12" rim and tire, how about a mounting it underneath the trailer on the back half? Same concept with 1/2" long bolts and large fender washers, but drill the holes in the floor. You could have it up flush with the underneath of the flooring. I'd use four bolts if I went this route. It would definitely be out of the way and out of sight.