If you are not certified, do so first thing... you will be exposed to rental gear at that time... As a PADI course director (inactive for about 15 yrs now) I have found that owning my own gear is far more useful than one might think... my wife is a bit less avid a diver than I am, but she too owns all her gear, as rentals vary in quality and how well they are maintained...
Over the years we have seen that divers who do not own their own gear tend to dive far less frequently, and even cease diving altogether after about a year... so own your gear, all of it, eventually, and you will be far more inclined to dive..
If you are not Open Water certified, get that first, along with your mask fins and snorkel, and discover how wondrous it can be... then try out a variety of regulators and BCDs to find the ones that are most comfortable for you... also, try them in diving environments that you will be experiencing most often... for example, I live in Rhode Island, and dive in cold water frequently... I want my gear to function well in somewhat hellish environments, with cold water, deep dives, and murky water... if you will be diving mostly in warm clear waters, then some features may be over kill...
As others have said, unless you plan on diving around your home area, frequently, there is really no need to purchase tanks... I disagree about weights though... except for diving while on vacations, I much prefer to have my weight systems set up as I want them, rather than using rental systems that must be tweaked and shaped...
But otherwise, you have some good advice above... try stuff out, get waht is comfortable for you... and be sure to dive safely...
As others have said here, the first things to get are your mask, fins, and snorkel... after that, a regulator and BCD are important... You get used to how these fit and work, and can have far more confidence in the maintenance history of them...