A workbench needs to be heavy enough that it doesn't move under you while you're working, and stiff enough that it doesn't rack itself to pieces under the forces that will be placed upon it. It doesn't take many hours of planing a board or hammering a chisel for a worktable made of nailed 2x4s to come apart. Traditional bench designs use mortise-and-tenon joinery, which is strong and rigid, but not really suited for a novice woodworker who doesn't already have a bench.
Remove the jaws and route the edges that you could not route while they were still attached. Then use a roundover bit on all of the corners except the inner edge of the inner jaw of the end vise. Give everything a lite sanding, and apply Danish oil to the inner surfaces of the jaws. (By "inner surfaces", I mean those surfaces that will not be accessible when the vises are assembled - the inner surface of the inner jaw, that bolts to the bench, and the outer surfaces of the outer jaws, that bolt to the vise plates.)
Before you start cutting or drilling the pieces that will make up the top, determine the layout of the top. This should include the dimensions of the MDF, the dimensions of the edging, the locations of the vises, and of the screws or bolts that will support the vises, and of all of the benchdog holes and of all of the drywall screws you will use to laminate the panels,
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After I left the magazine for a new job, I did all of my woodworking in my small two-car garage, but it was a struggle. Power, lighting, and temperature control were limited. And because I shared space with our cars I was always moving machines around, often while in the middle of a project. On top of that, my tool and machine collection had long since eclipsed the space. For all these reasons, fixing up the garage wasn’t an option. My finished basement is a family room, so it was out, too. An addition to the home or a stand-alone building would have been too expensive. I had to find a better path to a shop.