The Arcade version is the base model. Comes with all the basic equipment you need to play (the console, a controller, 4GB memory). That's about it. Elite comes with additional accessories (such as an exponentially larger storage drive) and HDMI support. Both versions have online support.
If by "modded" you mean an Xbox360 that isn't using proprietary firmware, then you can play original games but you can't use XBOX Live, you have no warranty and certain games won't work. Don't be an idiot and just a retail model.
If you have the money for it, go for the Elite or the 250GB Slim model, the slim is more but preferable for airflow if you have any plans for playing online (or downloading DLC, etc) just go straight to retail, don't bother with unofficial models, you probably shouldn't in the first place regardless. if you only play every now and then and aren't going to download much go for the 4GB version, and you can always use a flash drive or a SATA harddrive or just buy an Xbox specific one online, occasionally you might find one for cheap. All in all though, my personal recommendation from experience would be the 250GB Slim
Don't buy an Xbox. Geting one ruined my life. I failed my GCSE's because I played Halo instead of studying and I beame a mega ultra hypergeek and lost some friends over the PS3 vs Xbox 360 war. Stupid? Yeah. Do yourself a favour and DON'T BUY ONE! Waste of money and time.
>>13 Unless you're joking, let me say this. The XBOX didn't ruin your life. You did. Blaming something that you used makes you out to be a fucking retard.
Wait. Dont get the Xbox 360 Elite or Arcade. I heard that Xbox is making a new system and it should be coming out in the 2013-2014 time span. There has been some misconceptios on what it will be named but so far googling Xbox 720 seems to get research hits.