Your question covers several different topics but I think what you're interested in is Harmony. This is a very vast subject. As for the importance of what you lack as a rhythm guitarist, it largely depends on the style you play.
Lots of artists just don't know what they're doing when writing stuff and just happen to know empirically what goes well with what. In some styles like ska, punk or metal, a deep understanding of harmony is not mandatory, and learning a lot of tunes of this genre will give you a basic understanding of the underlying harmonies.
The basis of understanding which chord goes well after another is known as scale harmonization. You don't need to know how to do it perfectly, just to do it once or two to grab the idea.
You should find many many tutorials, here's one.
Don't be deterred by the relative difficulty of it. Depending on how your brain is wired it might seem quite hard to do, but you won't need it on a day to day basis.
As a result of scale harmonization, for each note of the major scale, you've got a chord (major or minor). You can shuffle through each chord of the seventh, and it will sound ok.
In C, the chords are C, Dm, Em, F, G, Am, Bdim.
Now each one has a particular weight, a particular sound, or effect if you will, not only in association with the tonal center, but also to the previous and next chord.
For example, the degree I feels at rest, and most song will end on it. The V pushes the ear toward the I or the IV for example. Switching to the VI will go minor. For example a really cheesy progression would be I, IV, V. The bridge could go VI, III, V for example.
(this is a very basic explanation with lots of weakness but I think it's a good start).
There's a set of very common chord progressions. Some of them have even names (50's progression etc, I don't really know them in English).
What I like to do is learn the songs I like, and transpose them to C (for the sake of simplicity). Then I try to identify the chord progression. This way I can tell what I like about this changes. You can also tweak each chord in certain ways, some of them are done very frequently. There's rule for that, but you can just learn empirically (for example, you can play the IV and then the IVm, I've found this many Muse songs and I like the sound of it, so I use it in my compositions. But it doesn't work with the V for example :)
To further describe the way each degree is attracted to another, let's take the V. The reason why the G7 (V) push toward C7M (I) is the following:
The seventh of G is F; its third is B.
The third of C is E; its root is C (obviously).
It means that two notes of the V chord are only one semi-tone apart from those of the I chords. A semi-tone interval is a very strong one, it is so close that the ear "wants" one chord to resolve to the other.
If you try to do harmonization by yourself, you'll find that each chord has also a seventh, which can be major or minor. As for the other extensions (6, 11, 13 etc), this is also a very vast subject. Know that each degree of the harmonized scale may or may not be extended with each scale note.
For the technical aspect of rhythm playing, I would advise you to take a look at my answer to this related question.
On a side note, while I agree that rhythm playing is linked to your abilities as a lead player, it is still another topic and this will not necessarily solve your problems.