A great console... although for newcomers to the Xbox 360 the 60Gb premium version is better overall value, especially if you own a HDTV, as the HDTV cable is not included in the Arcade SKU.
The premium version also features a 60Gb HDD which will allow you to install games from the DVD disc onto the Hard disk. This both reduces the noise of the console during gameplay and improves loading times a little for most games.
(The install game feature is included in the latest console update, available via the Xbox Live online service or from Microsoft directly if you have no internet connection.)
If you are undecided between the Xbox 360 or PS3, i would decide first if you require a Blu-Ray player or not. The PS3's Blu-Ray abilities aren't the best on the market when compared to some standalone players now available; however, you yourself may consider an average Blu-Ray player better than none at all.
On a final point, people that say the PS3's graphics are better are somewhat mistaken. What represents good graphics IS in the eye of the beholder, but from a strictly (unbiased) technical standpoint, the graphics performance in nearly all multiplatform games to date is actually better on the Xbox or to a lesser extent exactly the same on both consoles.
If you are looking for the best 'Games' console i would recommend an Xbox 360 over the PS3, with more games available for the Xbox 360, the console price difference just sweetens the deal.