I will try to keep this brief as it is rather off-topic, but as someone who did technical drawing at school in the 70s but never used it, and then went on to do 3D CAD as a job I might have some perspective.
Don't think about 3D CAD as making a drawing so much as making the part. In fact it can sometimes be helpful to design the parts exactly as they would be machined. The fundamental operations in 3D CAD are revolve (lathe-like) and extrude (mill-like).
Unlike with a real machine tool you have the choice of adding or subtracting material, rather than just removing. Usefully for making foundry patterns you can add a taper to the extrude operations for pattern draught. (The CAD tools also tend to have tools for adding draught to faces for this reason, but these tools might not always be able to "solve" the geometry)
With engineering CAD you mainly use a dimensioned / constrained sketch as the basis of the operations (this is not the case in animation or flowing-shape product design). You can constrain lines to be tangent to each other or at right-angles etc, which is nice because the computer does a lot of the "solving" of the shape for you.
If I was modelling the spider I would first draw a sketch of half the cross section of the rotationally symmetric part, then revolve it to get a plain funnel. I would then create another sketch plane on the open end, sketch a couple of circles linked by arcs, (dimensioned from the centre of the funnel) and extrude-cut that to make one hole, then pattern that x3 rotationally. The bosses would start from a sketch plane offset from the end of the funnel by the 1" dimension, again a circle dimensioned from the centre, and with a construction line from the previous hole to give an angular constraint. Extrude the correct distance and another rotational pattern. Then run round all the edges with the fillet tools to finish. It's literally 10 minutes work. Probably 45 minutes if you are getting the dimensions from a part rather than a sketch or table.