I recommend Roll20 and/or Google Hangouts for online games. I've been running/playing a campaign with my home group via Hangouts for a few months now, and using Roll20 when we really want maps (though D&D 5th Edition can be played without maps; a.k.a. "theater of the mind"). Roll20 also has a built-in dice roller, which is good if you don't necessarily trust your players as much as I do mine. ;)
The Basic Rules are available on WotC's website, as other people have said. It doesn't have character creation rules, though, if I recall correctly.
The D&D Starter Box set is a good purchase, too. It has the basics of the rules as well as a pretty good adventure, Lost Mine of Phandalin
, that could keep your group busy for a while. It also comes with a good-quality dice set. The price is really good for what it gives you: https://dnd.wizards.com/products/tabletop-games/rpg-products/rpg_starterset
(That said, it
doesn't have character creation rules, either! The only place you'll find them for 5th Edition is in the Players' Handbook
If you're in need of adventures, you can find a ton of them in PDF format on http://www.dndclassics.com/
They're almost all for older editions, but you can still take all of the adventure content and just give them 5th edition statistics.
You can find 5e-ready adventures written by third party authors on DriveThruRPG.
Personally, I would recommend looking up the OSR (Old School Revival/Renaissance/Rules) blogs and looking around them for inspiration if you need it. They're generally dedicated to earlier editions of the D&D rules, but I think you'll find yourself getting a lot of ideas from them anyway, and conversions are usually pretty simple; the OSR are usually a fount of inspiration. A lot of them connect at http://osrgaming.org/forums/
There are several "retro-clones" online (legal copies of earlier editions of the game) free for download that you might find to your liking, and/or if you don't have the money to buy up the current 5th edition rulebooks. Some notable versions include Labyrinth Lord
, Swords & Wizardry
, Basic Fantasy RPG
, and others. Google them and I imagine you should find them quickly enough.
Check out +Dyson Logos
if you're looking for good blank maps to use for your own dungeons, ruins, and other sorts of D&D-adventurey places. He has a Patreon account, too, if you find his maps useful.https://rpgcharacters.wordpress.com/
If you feel like getting involved with it, there's even an Adventurers' League community specifically for online play.
Here's the regular Adventurers' League community; they break them down further into regional areas:https://plus.google.com/communities/112559314186117492998
And here's the AL Online community:https://plus.google.com/communities/104095669932028051654
Hope this gives you some ideas. Welcome to the community of gamers, man!