I used an old fireplace small/med log rack for my barrel grate. Size is perfect for my needs, and since I don't weld, was quite simple. (Others have used various things such as angle iron, rebar, street grates. There have been various threads, recently that have had some pictures. I'll see if I can find them and then link.)
I don't have pictures of how I bricked. However, I used a combination of full size and half-size fire bricks. I've typically placed the grate in getting it as close to the door as possible. I have then used full-size bricks to create a wall (for the arch) at the back leading up to my stack outlet. Because the fireplace rack has a lip to it, I've used full size bricks resting on the edge to start lining the firebox. I've then added in half-size bricks to fill in as many open areas as possible. Typically, I've used the half-size bricks after the first course in the firebox as they stay in place better. I've also put half-size bricks on end at the front, on either side of the door opening, and between the end of the fire rack and the main arch-wall to fill in that space and help funnel the heat.
Good luck.
~Janet
2019 - 6th year sugarin'. 2nd year using propane. 13 taps. Just over 3/4 gal syrup. Light in color and flavor.
Intent to build a new barrel evaporator with my son this summer. Still don't weld. We'll see how it goes.