There is no order. If you want to learn since the beginning of computing then you flow kinda works. But in your flow, you need to be am uber nerd and also ASM instruction set is CPU specific making it bad for beginners. However C might be a good starting point since it is universal.
My flow is:
Python (well, anything scripted, loose datatyping)->Java->C++->C->ASM->logic gates
Reasons being as follows:
Scripted languages are really easy to pick up. A few lines and you have instant gratification.
The teach you basics such as looping, control flow, functions, OOP and classes with scope.
Java because it introduces more strict datatyping, forces OOP, syntax looks more like lower level, etc..
I think Java, even C# could be a gateway language, a better curve if you will. Plus with the scripted language understood, you will pick up better on what something like Java needs.
C++ because it us closer to the metal. This is one of the most used. Also it is compiled. It will teach better on datatypes, debugging, inner workings on programming and compiling, etc... If you code and concider yourself a programmer and want to be well rounded, you have to know C++.
C because of the reasons listed above except for the OOP stuff. C is much closer to the metal. You can go from 8bit microcontrollers is 64bit modernday computers. It is fast, and teaches a lot. Memory managment, heavier use of pointers and actual RAM locations and allocation, forced error checking, etc.. Did I mention no classes? All functions.
ASM because the most bare metal you can get before stepping into EE. All the reasons stated above with C, but with raw stack usage. With assembly you need to know how and why a computer actually works.
Logic gates are not needed for a software person. But will teach you exactly how a CPU is built and how memory works with it. Not to mention how everything else fits into play, from the northbridge buss, to the keyboard. This steps on the electron level and if you wanna be the one true master you need to at least be familiar. NANDtoTetris will teach you.