For making very precise wooden ware that resists bowing, cupping, twisting, or any other wood maladies it's not so much about the species of wood but the selection. I buy excellent pieces from big box stores all the time but the key to it is you have to be willing to go through the stack of lumber to find what you are looking for.
Here is the thing. What you really want is a quarter sawn board. But nobody quarter saws lumber out of timber for a reasonable cost anymore. To reduce waste and increase profits most lumber mills plain saw the boards.
Here is the difference in a quarter sawn lumber all the cuts pass through the center of the tree. What this means is the growth rings on the end grain will be perpendicular to the board. With the grain oriented this way the board is much more dimensionally stable and will usually resist cupping or bowing. They still might twist if the lumber wasn't stacked correctly so be sure to look down the board from end to end to verify relative straightness.
In plain sawn lumber they just cut a slab out of the tree then move the saw down and cut another slab and then move the saw down and cut another slab. This means that MOST of the boards have the grain running kind of in an arc that is more or less parallel to the board (when looking at the end grain).
But here is the good news, and the point of my lesson. Even in inexpensive plain sawn lumber the saw will pass through the center of the tree at least once. So one board in the stack will have the very center of the tree visible on the end grain with growth rings radiating outward perpendicular to the board. So in essence one board in every plain sawn tree is actually quarter sawn!
The box stores charge the same for the good board as they do the crap ones, so take your time in selection and become educated on how to identify the good one.
As for species, I dabbled with cedar early on and ultimately decided that it wasn't worth the cost. The best bang for the buck is to find that one magical quarter sawn board in white-wood. That's what the box stores call it anyway. In reality the mill has labeled it S-P-F. Which means it's either spruce, pine, or Fir. Any of these are suitable. Spruce is light and strong, pine is middle of the road, and fir is usually heavier but also has tighter grain and thus is stronger.
I do spring for cypress for the bottom boards because they last much longer and it's good economy.