I too would go with the majority vote, the Pro but each system has pros and cons.
Arcade:
Pro's. Cheapest of the lot gets you into next gen gaming for a very reasonable price yes the Arcade does come with a memory stick and wireless controller where as the core had no memory device and a wired controller
Con's. Upgrading the hard disk to the 20Gb or 120Gb in the future costs an arm and a leg
No backwards compatibility (Hard Disk required to download the required patches)
No Opportunity to download the vast ammount of demos from the xbox marketplace (again the Hard Disk is required) which are invaluable when it comes to routing out the good from bad games.
Only a standard composite tv lead (with Scart Adaptor)
Pro:
Pro's. Mid Priced of the SKU's not a huge ammount more money for what I would call an almost essential couple of items. (20gb Hard Disk, Online Headset, TV Lead)
20Gb hard disk included enough as said before to try out demo's play the old Xbox games
Even get the odd film rental from the xbox marketplace
Standard & HDTV Component TV lead included in the box
Con's. That extra bit of money could get you a good game or two
Elite:
Pro's. 120Gb Hard Disk, Plenty of space for everything you'd ever need to download (Patches, Demos, Marketplace Films & TV Shows (Although you have to pay for these))
It's Black and looks more in tune with most modern TV's and audio visual equipment.
Con's. The Price
Since all new 360 consoles come with the HDMI port on the back of the machine the only extras you get are the colour, the Hard disk size, the hdmi lead as well as the TV/Component lead from the Pro and an adaptor to get optical sound out.
All in all it's your choice, but I don't think you'd go far wrong in purchasing the pro
One thing to consider with regrards to using your 360 online, to download patches and other content, that noone else has really considered is that to get your machine online can cost a small fortune on it's own. This comes down to where you are phisically going to be placing the unit. is it going to be close to where your internet connection comes into your home & what sort of connection speed do you have? To be honest theres no point going for either of the hard disk models if you only have dial up you'd be waiting forever for any content to arrive. Next off is do you already have a router? is it wireless? If the xbox is going to be close to the router then thats not too bad, a RJ45 network lead come's in the box at least with the Pro and Elite, simply plug the cable in and your away. If you plan on using Wireless then expect to fork out annother load of money on the adaptor for the 360 as it has no wireless network capability out of the box.
Edit: Content