In my opinion, only a super computer is good enough for flash/facebook games or youtube videos. Flash is bloated and slow, as is just about everything Adobe makes.
Flash games will run about the same on any MBP. They will use a lot of the CPU time, make it run hot, and kill the battery life. It won't make much difference if you have the 2.26, the 2.53, or a 3.06 GHz CPU.
Flash video might be slightly better on a 15" MBP with dedicated video card, but I don't know if Flash does hardware decoding. It will probably be OK on even the 2.26, though.
The 13" can play somewhat new games, but likely at lower graphics settings (low resolution or low quality and detail). The 15" with a Nvidia 9600 graphics card will be significantly better for games, though the 9600 is getting kind of old compared to desktop cards or even the cards in PCs. You will need to install Windows to play most games (except flash games, of course). You can install Windows in Bootcamp then choose between OS X and Windows when you reboot.
You probably won't notice much difference between the 2.26 ad the 2.53. The 2.53 is only 12% faster, and I would get the 2.26 just to save money unless you need as much speed as possible.
Another big limitation of the 13" is the screen resolution. 1200x800 is fairly low, and a bigger screen will be better for multitasking. The 15" is only a bit better at 1440x900, and the 17" is a big step up at about 1920x1080. (I don't know if all these resolutions are exactly correct). The 17" is big and bulky, though.
With 4gb of RAM, the 13" is a good computer, and it is just about as capable as a larger MBP, except for the lack of dedicated video card and the low screen resolution. There isn't much it can't do besides what I listed here, and even everything I listed here will work, it's just that the experience might be better with a different model.