Below is my little project to make a Barbeque.  The entire project took about 6 days to complete (though from start to finish it took about 3 weeks)

I started out by enlarging an existing concrete pad.  The combined slab area was increased to an area of 3'-2" x 6'-0".  Next was the placing of the concrete block that would make up the walls of my BBQ.  I chose 6x8x16 gray conc. block as the material for my walls. These will be covered with used mini-brick.   Below is a conceptual rendering of my BBQ.   

(Originally I was going to use a ceramic tile for the top but opted for used brick instead.)

The next step in my little project was to level and fasten the sub base for my used brick top.  I decided on using 3/4" plywood as a base with an additional piece of 3/4" plywood fastened with screws and glued to the underside of the area where I was going to cut out an opening for the BBQ drop in unit 

Once the plywood was leveled and grouted into place I was ready to start laying brick.  I used bull nose bricks across the front and back of the BBQ with common used brick through the rest of the top.

The following are some pictures of the project in various stages.

I decided on the Turbo line of barbeques from Barbeques Galore

It seemed to have the most features for the price.