500GB would be more than enough.
I don't have ALL the information, but from the past month, I've been going through the exact same thing. I've been wanting to get an Xbox 360 so I can play a bunch of games that I can't on Steam (PC). But I'm gonna have to hold out on getting one because I have college and won't have time to play anything.
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(A lot of this information pertains to what I know about Xbox 360 and not so much Playstation 3)
So first.
Console: Which would you prefer Microsoft (Xbox) or Sony (PlayStation)?
Looks? Black or White? Size of the console?
What I'm going to suggest is getting a last generation console i.e. Xbox 360 or Playstation 3.
There are 3 different styles of Xbox 360 and 2 different styles of Playstation 3.
X360 Original, X360 Slim, and X360 Elite. PS3 Original and PS3 Slim.
Xbox One and Playstation 4 are current generation consoles. Those consoles pretty much just give you better graphics and a different controller. Plus a $300-$400 price tag. I'd stick with the older console.
Controllers: Think about the controllers. Xbox 360 controller is my personal favorite. PS3 is nice. But it's really up to you. Perhaps go to a Gamestop or other video game store near you and hold the controllers and see which one you like best. Get the feel for them. I would also suggest always go for the wireless controllers. It'll save the hassle of cords. Just go with wireless.
HDMI: Do you want to play your games in HD? You can play games on either console without HDMI using just regular AV cables and the games still look good (Wii also uses AV cables for reference). From what I've seen looking around, Xbox 360s come with only AV cables, but you can get an HDMI cable for less than $10.
Games: What games are you gonna play? If you're probably only gonna play Disney Infinity 3.0 or LEGO games, you'll only need a smaller GB space. Maybe 4 GB to 60 GB.
If you want to play games that I would, Batman: Arkham City, Call Of Duty (any of them), or Splinter Cell games, i.e. action/adventure games. You're going to want a big hard drive space. 120 GB to 250GB or even 500 GB.
NOTE: A loooooot of the games on Microsoft and Sony consoles are not "family friendly" games. If you want to play games geared towards a family, I would suggest getting a Wii U.
What I'm going to suggest is get an Xbox 360 Slim 4GB.
http://www.amazon.com/Xbox-360-4GB-Cons ... B003O6JKLC
Then buying a 250 GB hard drive. (And just switch out the hard drives.)
http://www.amazon.com/Simtyso-320GB-Int ... op?ie=UTF8
If Xbox isn't your thing, look into PS3. Look around. You want to find the best console for you.
When you look around online or wherever you look for it, make sure your console has a controller and cables. Because people will sell their consoles with only the console and none of the other accessories.
Or you could buy them separately.
Hope that was helpful. If you have any other questions, please let me know.