The only real differences from the E7400 and the E5200 is the stock frequency (2.8Ghz and 2.5Ghz), the E7400 has 1mb more L2 cache as well. The E7400 also has a faster FSB speed.
You can go with the Gigabyte, Asus, or Foxconn board... they are all good.
You might want to go with the E5200 to save some money, and any RAM module suggested will work fine.
The mobos suggested have enough graphics power to play basic flash and 2-D games... maybe some low-end 3-D games. What are you planning on playing?
As stettybet said, you should get a new PSU as that will make your system more stable and reliable.
If you got the E5200, Gigabyte board, Mushkin RAM, and the OCZ PSU... you would have spent $193.
Leaving around $60 for a graphics card.
You should get either a Radeon HD 4650 or 4670http://www.newegg.co...N82E16814125253
This card will push you budget a little: http://www.newegg.co...N82E16814125277
If you are going NVIDIA, then a 9500GT or 9600GSO will do it.http://www.newegg.co...N82E16814121320http://www.newegg.co...N82E16814130378
Those cards are just a couple... look around yourself and read some reviews to find out which card is the best for you.