This desk can be made for about $30 worth of wood, a piece of glass from Ikea (transparent gray Malm glass top, 18 7/8x63"), some screws, and some paint. About $70 total. The frame is extremely light, but very sturdy with the top on it.
Step 1: Legs
2x - 1x3x30"
1x - 1x3x17 1/2"
1x - 1/2x17 1/2" dowel
Glue and screw the pieces together, short pieces sandwiched between the long pieces; the dowel is about 4" down from the top edge
Step 2: Bookcase
1x - 1/2x11 3/4x18 1/2" plywood
2x - 1/2x12x18 1/2" plywood
1x - 1/2x12x30" plywood
1x - 1/2x12x22" plywood
1x - 1/2x18 3/4x30" plywood
1x - 1/2x10" dowel
4x - 2" corner braces
The box of the case is formed with all of the plywood pieces, save the 11 3/4x18 1/2" piece. Using the picture as reference, the back is 19x30", the left side is 12x22", the top and bottom are 12x18 1/2", and the right side is 12x30". Glue and screw those pieces together.
Glue and screw the dowel through the top, about 3/4" in from the front and left side edges.
Drill the holes for the corner braces, which will support the shelf, so that the top of the brace is at 11" from the bottom; 2 braces per side.
Step 3: Top Frame
2x - 1x4x63"
2x - 1x4x12"
Glue and screw, sandwiching the short pieces between the long pieces
Step 4: Frame Assembly/Painting
Paint the whole thing; don't forget to paint the removable shelf.
Install the corner braces.