Lots of good advice so far. 
5/32" toggle bolts on the lower part should be more than sufficient. The weight of the unit plus the weight of pots, pans, etc. will be pulling straight down, and pushing back.
For the upper (center) support, finding a stud is by far, your best option. The entire weight of the fixture, plus the weight of whatever you hang on it, will be pulling out, away from the wall
For that, I would recommend using a #10 Pan head, wood screw of sufficient length to enable at least 1 to 1-1/4" of penetration into the wooden stud. (1-3/4"" ought to be more than long enough. If you’re unable to find any screws that size, I would err on the side of longer=stronger.) Most houses use 1/2" sheetrock on interior walls, as such I would be hesitant about using Molly bolts or toggle bolts for the top support, if you’re going to count on the sheetrock alone.
If for some reason you’re limited on where (horizontally) you can position the unit, another option would be to mount a 1"x4" to the wall with toggle bolts (or, if possible, make the 1x4’s long enough to catch a stud on both ends, and use screws to attach) and then mount your hanger to the 1"x4" 's, with wood screws.
The unit pictured looks like it will hold up a substantial amount of weight, if fastened properly.
I realize that what I’ve described might sound like “overkill”, so here’s a suggestion.
Put all of the pots, pans, skillets etc. that you anticipate hanging on this rack into one stack, lift that up and you’ll have a good idea of what will be hanging over your head. (Plus the added stress of removing and replacing said pots, pans, etc. can cause fasteners to loosen.)