I'm new to Xbox so please bear with me as I'm primarily a PS3 and PS4 user.
My wife won an Xbox One and I bought an Xbox 360 recently for $10 so I figured I'd buy a year of Xbox Live to take advantage of Games with Gold. My 360 didn't come with a hard drive unfortunately. My question is this: On my PS3 or PS4 I can redeem the monthly PS+ games but I don't have to download them. As a matter of fact I can redeem them on their store website so that I can download them later. Is this an option on Xbox 360? Every time I try to redeem a game on the Xbox store it just tells me I don't have enough space. Is it get a hard drive or miss out? I'd like to have them available to me when I do get a hard drive, as is the case with Sony.