When I build, I use a simple principle. I keep parts as large as possible, for as long as possible. I only make cuts or plane surfaces that are essential to the task at hand. This accomplishes two things. It gives you the opportunity to correct small errors, and it prevents you from making errors by keeping your mind focused on simple, individual tasks. This is especially important when building something for the first time. As this is the first miter jack I've built using this design, be warned that I have not had a trial run. I'm as green as you are if you're building along.
First thing is to mill the stock for the base, which finishes out at 1-15/16" thick. If you choose good straight stock, and tell your yard not to hit or miss it (skip plane), you can likely get that thickness from 8/4 stock. If not, you'll need to laminate, or use 9/4 stock at least. I began with 12/4 hard maple, and sawed about 3/4" off the thickness (each face) before milling it to 1-15/16". I did not have access to quartered stock, but if you do, definitely use it. It will make the base very stable.
After milling, layout the large rabbets on the spacer stock and the two body sections. If you use a table saw to cut the rabbets, you only need to layout on one end of each board.
The rabbets are 13/16" wide and 31/32" deep. The latter dimension centers the rabbet on the stock's thickness. Note that the spacer stock is milled to final width, and is the full length of the other body pieces. More on that later. The two body pieces have not been milled to final width.
If you use machinery, the table saw excels for cutting the rabbets. With only four to cut, I didn't bother mounting a dado set. I like the more controlled results I get with the two cut method anyway. Especially with these very large rabbets in hard maple.
It's best to cut the rabbets a tad small, then dial them in with a shoulder plane. If you do this, make absolutely sure your iron is set parallel to the sole. It's all too easy to go past 90 degrees, even with just a couple strokes. The trick to using a shoulder plane in this situation is to take as much of yourself out of the equation as possible. Use your leading hand to firmly press the toe of the plane directly into the rabbet's corner. Now use your other hand and push forward only. Don't grab the plane with this other hand, your leading hand is the steering wheel, and your other hand is the gas pedal. If your iron is sharp (it better be) the plane will jig itself into the rabbet and make it dead square with successive passes. I like to take many light passes with a rabbet plane. It may be slower, but I can be extremely precise.
Here you can see that I've got to take a couple passes either on the top edge of the spacer stock, or on the side of the rabbet in the body section. I took a couple passes on the spacer stock with a bench plane to get the fit right.
A good fit on all three surfaces. It's not entirely necessary that you nail a certain dimension here. So if you need to make the spacer a little narrower to get a sweet fit, do so. Good joinery is more important than an arbitrary number.
With the spacer stock in place, mark for the final length of the body, and for the length of the two spacer piece at each end. There's a minor mistake in the Sketchup drawing. The spacer blocks are both 3-1/4" long, but in the original jack the spacer block on the nut block end is 3" long. It won't affect anything on the vise, so I'm leaving the SU drawing as-is. I did mark my nut-end block at 3".
Next, cut the spacer blocks from the piece, but only cut the inside end. Leave them long for now, like the body pieces. You will cut them to final length after gluing them to the body pieces. You will want to sand the ends of the spacer blocks now, before glue up.
The remainder of the spacer stock will get used for the jaw spacers and retaining blocks.
Glue up the base assembly, carefully aligning the inside ends of the spacer blocks with the marks on the body sections. The ends won't necessarily be flush, since all pieces are over length. I made two special cauls with relieved mid sections so I could draw up the spacer blocks tight into the rabbets. Make sure when you apply glue that you glue not only the rabbet in the spacer blocks, but also the lower edge that fits into the rabbet on the body pieces. I realized a few minutes after they were in the clamps that I had only glued the rabbet in the spacer blocks. I'm not worried about the strength, since these blocks don't see a whole lot of stress. The splines at the end will help reinforce as well. Still, don't make my mistake.
The jaws are glued up from 12/4 stock, or thinner if you need to. The original is finger jointed. Feel free to do this if you like the look. I'm not convinced it adds any strength if you can make a great glue joint.