Well, i wouldn't recommend someone to learn OpenGL 1.3
due to absence of GLSL, which it came in OpenGL 2.0 as GLSL 1.1 which version i still use as well.
GLSL is useful but when you're learning i think it is better to have things on screen as fast as possible and learn things in a step-by-step fashion, so personally i'd suggest learning how to put some very basic models on screen first - something like making a planetary system with planets rotating around a "sun" and some of them having some moons and then having a light and a texture. This will teach both general graphics concepts like how matrices can be used and combined (without needing to deep dive into how they actually work at that point) and some OpenGL stuff that will be used later (creating objects - in this case texture objects - and deleting them, loading data into them, binding them, etc).
Then once there is an understanding with that, one can move to writing a shader to replace the fixed function lighting with their own, without also having to struggle with resources, objects, etc. But still using GLSL 1.2 (or less) so that they have access to the fixed function state (so adding support for shaders will be a minor drop-in work).
Then as a next step after that, they can start replacing piece by piece the functionality that OpenGL 1.x/2.x provides, starting with the matrix stack - replacing the glPushMatrix/glPopMatrix that they used to make the planetary system with their own matrices using glLoadMatrix (so their existing code, including GLSL shaders, still work) and having their own matrix stack.
Then move on to replace glLoadMatrix with glUniformMatrix but still on GLSL 1.2. After that they can start getting rid of the pre-2.x stuff, move to core and use more recent GLSL versions.
I think this is a better and much easier way to learn OpenGL because you have working results soon and you only focus on one thing at each step instead of having to learn everything in one go.
Though i think that after you reach OpenGL 3.x there isn't much of a point of going to the 4.x stuff sincethey were largely about doing the same stuff as before except faster. At that point it might be a better idea to switch to Vulkan since i think that if you need the 4.x stuff, Vulkan can actually be simpler (even if more verbose).
To this day, AMD's official drivers cannot draw lines using 1.x paths without leaking a shittonne of memory.
Do you have any example of this? All of my tools (and i think Blender 2.79 too - which i'm using myself - though i'm not 100% sure) use lines with the glBegin/glEnd stuff all the time and i do not remember ever having any memory issues (i'm using AMD). Line drawing is much slower than on Nvidia hardware though, but that is another issue.