I guess it depends if you want to use the system for more than one game.
That's the main reason I haven't picked up a JPN Xbox and L4U, I just didn't see it as worth it for only one game. That's why I like the PSP version, I could get more use out of the PSP than just for one game. If I was rich, I'd probably get the xbox version for the better graphics. However, like H4 says, 90% of the experience is already in SP. Each version definitely has it's positives and negatives though.
Office Mode is probably the best selling point of the PSP version, so I want to emphasis that. Well IMO because even if you can't understand Japanese, this mode is easy to figure out since there's only a couple menus. I've spent a lot of time in this mode because it's just fun to play around in. You can pick any of the 12 idols (If you have 961 pro unlocked), so even if you don't want to buy all three versions of the game, you can still have access to all the idols. You can dress them up with whatever you have unlocked, pick whatever song, do an audition, watch a TV performance and take pictures/video of it there too.
IMO go the PSP route at least for a beginners experience.
Also I'd probably suggest waiting till February if you go the PSP route. I read it's going to reach greatest hits status at the end of January and become cheaper to obtain. Playasia has pre-orders for it for 35 bucks, which is 14 bucks cheaper than the asian version. If it also becomes available on the JPN PSN, you could actually just buy a PSP, create a JPN PSN, and buy a 5000 yen PSN code off the internet. Then you could just download the game off the PSN and use the remaining yen to get some DLC.