I need to know what looks good, and why. It is important that I know why it looks good so I can use that knowledge in future projects.
I understand a lot of design is up to the individual, but I would like to think there must be some general universal rules as far as graphical aesthetics go.
This question crops up here from time to time, and no doubt others will link to similar questions. I think, however, that you touch on a very important issue.
We have a post here with resources for design beginners. It certainly applies to web as well.
Yes, there are rules-of-thumb for web design and web aesthetics. What is tricky with web is that it is entirely dependant on usability. Unless you are making a one-page leaflet site, all web design must start with an understanding of interaction design, information architecture. Since you are familiar with JS, HTML and PHP, you obviously have a fair idea about what data looks like at the back-end. The magic is to create that bridge between – essentially – databases and user interface. Some websites bases their front-end on the obvious structure of the back-end. This is often logical, but very often not particularly user friendly, intuitive, visually pleasing, visually intelligent or efficient. And certainly not fun! Either to make, build, create, design or use.
For static design such as print, there are little or no concern about the linear use. Books, comics, posters, leaflets all have a sequential “story”. Web on the other hand, is mired in usability problems.
Usually, you will have to start with conceptual thinking on who is to use it, how will they use it, what will they use it for, and what information or data needs to be sequential or not. Every website are in a sense an engine to browse information in their own right. You can guide your users, or you can let them dilly-dally around in a more random fashion. All these choices will influence and in some cases direct the visual language.
It could also be worth sniffing at heuristics to get a feel for some usability criteria:
Interaction design principles:
Combine a basic interaction knowledge with the design principles outlined in the first link would get you very close to sensible and interesting web design.
(as a slight aside, here is a post about design relating to programmers. I think it is well worth a read
How do I learn to be creative
This was maybe not entirely the direct answer you were hoping for, but I hope it can be of use nevertheless.