For someone that has little intention to play online multiplayer Xbox Live is indeed free.
For someone that does not have an HDMI enabled AV receiver (you do not mention if your 37" TV has hdmi) you may still need to buy component cables for the PS3 which come with the hdd enabled 360.
The xbox storage upgrade site is still active which means you could go the Arcade route and for a minimal cost get a hdd but you would need to purchase the HD cable for the 360 which will have your toslink out port on it.
It is not mandatory at all to purchase the official 360 wireless dongle; an ethernet bridge (like the original xbox wireless adapter) or any cheap router that can act as a bridge will suffice if wireless is mandatory, still this is an extra cost.
No one mentioned this but Live Arcade and Community Games, in my mind, will always be a superior service to PSN until such time as there are demos available for EVERY PSN downloadable game.
There are multiplatform karaoke games and platform holder karaoke games of which I have none so I cannot speak to the quality of any of them.
Indeed, OP, congrats on your purchase if your mind is made up, however I'd reconsider your choice. The general sentiment was echoed in a thread a while back - can't think of the link, possibly the Console Pricing Thread - however the general consensus among quite a few posters was that it was an unwise choice to recommend the PS3 over the 360 at this stage. The cost difference alone is staggering - I'm in Australia, where the PS3 is roughly the same price as in Europe - and I'd be paying well over double once everything is said and done, regardless of feature-matching. Then you have to consider that the added cost will generally get you inferior versions of the games you'll be buying.
Also note as per the post above, MS is basically letting you buy hard drives for next to nothing if you're a new purchaser, if that's what is swaying you.
Perhaps you'd be better off giving a detailed listing of what you'll be buying, and how much it would cost you, in each situation. That way, it will be much easier to see what's your "need to haves", your "nice to haves" and your "not importants".
Cheers