Well, if you actually got perfectly straight planks and boards...congrats, you are the first person ever to do so!

But really, what little can be seen in those pics seems to look like pretty nice lumber.
Wood is a natural material, each and every piece is unique with its own internal grain structure, and all of it wants to warp. The best you can do is take pains to choose wood carefully at the lumber yard. You won't be making any friends by doing this, but personally inspect each piece, sighting down the length of it to check for straightness in both dimensions. Also watch out for pieces that are twisting along their length. The dryer the better.
When building the stand, use wood glue and screws, and always clamp the pieces together to ensure perfect alignment (the clamp in your picture is the perfect type). You can also get a specialized clamp that makes perfect corners easier to achieve.
Also, the fact that you are using a mitre saw is a plus, but that doesn't guarantee that your cuts are perfect and square. If the saw is adjusted even slightly off 90 degrees then it will produce identically imperfect cuts all day long. And an inexpensive saw can have a notoriously unreliable and inaccurate gauge indicating the exact angle of the cuts. Since you are essentially looking for nothing but perfect 90 degree cuts, check one with an accurate T-square to make sure that's what you are getting. If you need to slightly nudge the saw adjustment this way or that to achieve perfection, do so...and then crank it down tight to keep that setting from changing due to vibration, etc.
Edited to add: Forgot to mention this, but if you bring home a dozen pieces of nice, straight, clear wood...and then lay it down on your basement floor or in the garage for a couple weeks before you use it...you may be in for a shock. A change in humidity, or laying in contact with a concrete floor that transmits water, can quickly warp a nice piece of wood into a pretzel. Buying wood that is as dry as possible and then using it up quickly is the easiest course of action to prevent this. Once it is assembled into the three-dimensional stand it should...
should...dry out without contorting itself.