Amazing - if I look back at when I bought my first SLR around 1972 or so, nothing has changed. Then - like today - there are those that believe they first need the greatest equipment they can afford before they can make great pictures and there also are those who warn you that a Stradivarius doesn't make you a great violinist. And both are right, in a way.
Maybe the best way to start explaining it is that the guy with the Stradivarius didn't get it before he had established his credentials as a musician on lesser equipment first.
So I would suggest following a dual strategy:
First of all, educate yourself about all the photography themes in a course, via a book or online reading. Learn about composition, lighting, the creative use of colour, and a bit about the properties of cameras and lenses (wide angle versus telephotos, macro lenses etc.) - none of this has really changed since the days of the first Leica. Consequently, books by such luminaries as Andreas Feininger (my first choice) or Anselm Adams still have a huge amount to offer (just don't go overboard with Adams' "Zone System" - it is still a very valid principle, but we implement that totally differently with today's computerized cameras.)
Secondly, get on some (almost any) digital camera soonest, so you can practice what you have learned. Start discussing photos with other people - yours, theirs, anybody's. Consider joining a camera club, You will find friends there that are on the same journey you are on, some ahead of you or even way ahead of you, some behind. A spirit of give-and-take should prevail.
Then, once you understand what all the features of a camera can do for you in your quest for the greatest photo of all times you can go out and shop for the best camera for you. It may be a dSLR, but it may not be. If you are like me you may end up with several cameras, each for a different reason.
Also bear in mind that if you choose a system with interchangeable lenses the quality of the lenses may be more important than the quality of the camera body. And you may upgrade to a better body later without having to also swap all your lenses.
I bought into such a system in 1979 and I upgraded to a more advanced body around 1990. That kit is still around and - especially - some of the finest lenses I ever owned are from that first day. Unfortunately for me, when my manufacturer introduced autofocus lenses they were no longer compatible with their older system, and no adapter possible (experts can now tell my house brand.) It didn't bother me then - who needs autofocus, right? But obviously, I wanted to go digital eventually and I had to make the break.
Today I still use all my old gems of lenses, but on a different brand of camera now. The industry came out with a sort-of standard called "micro four thirds" which has interchangeable lenses, but without the mirror and prism that characterize SLRs. As a result these cameras are much smaller and more lightweight, and the can use my old lenses with an adapter quite nicely. Now I find that when I travel the compact micro four thirds kit - without the old lenses - is what I take with me most of the time.
Ideally, there should be four types of camera in my life: the one in my mobile phone that is always there and should not be too shabby, please, the SLR for serious jobs, the micro four thirds for casual holiday trips and for serious work using my old lenses and, finally, a compact point-and-shoot of what I call the 10x10 category: at least 10 megapixels and at least a 10x optical zoom range. That one will be coming with me when I am expecting to take pictures that my phone isn't up to but I can't even afford to carry even the micro four thirds kit.
Having said all that, to try a direct response to your question "what am I getting myself into?" here goes:
It does of course depend on what sort of camera you currently have - is that point and shoot digital already or are you still using film? If you are already on digital and you use a computer to store and process your photos, possibly even printing one every now and then, then you are already a long way down the road to understand what will become of you. By and large, things are infinitely easier than they were in the film days, once you have familiarized yourself with the "computer business."
But photography has always been a game of accessories - SLRs and other "system cameras" much more than your self-contained point & shoots or bridge cameras. So expect to find a "need" or "craving" for an extra lens, filters, a separate flash unit, a tripod, more memory cards, etc. You will have to decide which items you need and you will want to ensure up front that "your system" will offer all of these.
That gets us to the difference between a dSLR and a dSLR. Contrary to what someone else said here there are vast differences in quality and features. Again, you will need to decide what level of functionality you will need, possibly up front. But then, when you choose a major name brand you can get an entry level camera and rather decent lenses and later upgrade to a more advanced body. Consider the speed of development in this market - there is a new range of cameras out roughly every year. So you may want to upgrade from time to time - but the lenses stay relatively stable, so you are well off if you can stay with the same brand.