I think you almost need to discover which Floyd fan you are: pre-DSotM, post-DSotM or post-Waters—or some combination of the three. (I maintain that every true Floyd fan loves Dark Side of the Moon). Each incarnation is quite different.
In the pre-DSotM days, the music was heavily Syd-influenced, if not written and/or performed by Syd outright. The music is more drug-tinged and spacey, less radio-ready (with some exceptions). The Floyd was most definitely on to something, but the rock world had yet to fully embrace it.
Dark Side of the Moon was their turning point, their creative zenith. It was the culmination of everything they had achieved up to that point, plus more. It had the concept, the creative energy, the experimentation, the musical genius. Total wow factor without ostentatiousness or absurd self-awareness.
The post-DSotM period represented a continuing maturity of all the ingredients contained in that seminal record. Each album was a conceptual microcosm, flowing seamlessly (quite literally) from track to track. You almost couldn't take a song on its own without feeling the presence of the tracks surrounding it.
With the departure of Roger Waters, you now have a Gilmour-led band that explored a lot of other options, including lots of side players and grander orchestration. Gilmour's sound, for better or for worse, became more processed and layered as well, almost symbolic of the entire band's new sound. They were even more radio-ready, but now it seemed almost as if hits were more the focus, less the by-product. (Some would argue that point.)
If it isn't obvious in this post, I like the pre- and post-DSotM Floyd, but not so much the post-Waters Floyd. I can't connect after Waters' departure. While there are some standouts to my ears, most of it falls flat.
After a few years of discovering and integrating Floyd's music, I'd be interested in finding out where you land on the map. It's sure to be an oiixing awesome journey.