EDIT: For people coming to this thread, there are good answers here that solve this question, so I can't say there's ONE correct answer. Thanks to John Burrill, Kevin Chandler and Maha Nadarasa!
Hello all,
Just wondering what type of shape/shapes creates this structure? I modeled it with a drafted square (since it has a 2 degree draft) and circle with those fillet corners. However, the intersection did not give the desired look the container has. I also tried to do a drafted square with fillet corners and make those "pocket" cuts which got me the closest result, but I couldn't get the "triangular" cutout to match on both sides to create that symmetrical effect.
How would you go about this?
usually where people learning solidworks get trapped is in looking at the edges of the part as something they have to figure out. You're worried about how you're going to get the saddle curve at the midpoint where you change shapes. That curve arises naturally from a cylinder intersecting an incline plane. So when you tackle these kinds of modelling challenges, look at the faces that define the part masses and the curves will take care of themselves.
There are a few intersection shapes you should learn to recognize.
That curve arises naturally from a cylinder intersecting an incline plane
so how do you get an incline plane to intersect?

The rest of it's pretty straight-forward drafted part guide lines.
Save fillets and draft for the end if you can (in the case of the main mass I couldn't)
If you have a boss that seperates from a drafted wall, using Delete Face to clean up the intersection is a good remedy
when you add fillets and rounds, do the large ones first and let face selection do your work for you where you can
If you're going to core this part out, then I'd suggest rolling the feature bar above the smaller fillets
I'm using 2019, so it doesn't look like it'd do any good to post the part back here, but hopefully that will give you some clues about approaching this kind of problem in the future.
Good luck.