Ahh, the power of the internet…
Muskateer, my advice:
1) Start reading the Fourth Edition DMG. Not for the rules. But for the advice, which is good.
2) Get the 1983/”Red Box” Basic D&D rules. Again, for the advice. Though you can also use some of the rules and adventure, if you want.
paizo.com - Dungeons & Dragons Basic Rules (1983) PDF
3) Get the following adventures: The Village of Hommlet and the Keep on the Borderlands. Start reading them. Decide if and how you want to use them
paizo.com - AD&D T1: The Village of Hommlet PDF
paizo.com - Dungeons & Dragons B2: The Keep on the Borderlands PDF
4) Start playing!
5) As Korgoth noted, start a little “loose”. Don’t worry about every rule, just get going.
6) Be careful with what people on the internet say (like me

). Its been a long, long time since most of us started, and we sometimes don’t remember what it was like all those years ago.
7)
Several months in the future…you might want to look at some other editions, including fourth, all of which are available as pdfs. Note that early editions basically work together (basically), but 3rd and 4th are sort of stand alone. But they have some advantages, like no THACO.

In the near term however, it is better to just play then get caught up in the details of this or that edition.