However if you are a sucker for cheap affermation and goals then you can kiss your life goodbye once the achievement system sinks its hooks into you. I never knew something so meaningless as a score that keeps track of how well you do over every game you play over the life of the system could suck so much time out of your life, but there it is.
As for the Hard drive space, yes you can upgrade if you need to, but if you aren't planning on downloading a ton of movies and tv shows from live marketplace you aren't going to need it. I have a friend that has the large version and he still has 100gb free. I have the 20gb, and even though I have over 50 of the arcade titles downloaded, and a ton of add on tracks for the music games, and so on, I still have well over 8gb free on mine.
As for wireless, I know the older models didn't have it out of the box(not sure if the new ones do or not). The older models you had to buy some sort of add on to go wireless. I'm sure someone way more in the know than myself about the subject will speak up.
As for games you missed. Where to start(and yes I don't get the whole Halo thing either).
There has never been this many good games on a system almost ever. If they keep up the trend into the last half of the 360's life, then it will be the best gaming system ever. That's over the PS2, SNES, and Genesis IMO.
Here's a list of games you REALLY should play on the 360(I'm assuming you don't have a PS3 so you haven't played any of the now gen titles.)
I'll just put the list in no particular order, and if something catches your eye you can ask, or wiki it
Call of Duty 4
Guitar Hero 2 and 3
Virtua Fighter 5
Gears of War
The Orange Box
Marvel Ultimate Alliance
Splinter Cell Double Agent
Rainbow Six Vegas
Call of Duty 2
Lego Star Wars 2
Tomb Raider Legend
EA Sports Fight Night Round 3
Ghost Recon Advanced Warfighter 1 and 2
That should get you started