How does this Xbox Live Silver/Gold thing exactly work?

Just bought this baby recently, and after some problems (And wailing (And perhaps annoying you) on here) regarding the PSU, i finally got one, and it is working pretty well!

And it also came with the 120GB HDD, the Xbox 360 Elite version!

Only problem is... this is something new for me, and not only because of playing with a gamepad.

As a PC gamer used to play games via Steam with purely digital copies that already have the complete Singeplayer/Multiplayer pack, i'll feel myself like lost by playing some Xbox games like Red Dead Redemption or the 360 version of GTA V

I already got a store where i can buy physical copies of them, but also DIGITAL copies. How do those exactly work? I buy the digital code card, redeem the code on my console, and the gamke gets linked... to my Xbox or to my Xbox account/gamertag?

Also, what if i buy them? I already got the privilege to play them online, or do i have to buy a Xbox Live Gold subscription so i can access the online functionalities? If so, then i'll find it unfair since i'll spend tons of money for an either physical
or digital copy of a game but only limitedly, since i can only play the single player capabilities. I am sorry, this is way too different from PC's Steam and so.

:)