If you're really wanting to game on the computer, you may want a little bigger power supply, although the 500 watt will probably run the system.. IN addition, if you're installing Windows 7 64 bit, then I would double the amount of RAM you've got.. The motherboard has four slots and you could easily put four sticks of the RAM you listed.. On the other hand, if you're installing a 32 bit version of Windows, stick with the 4 GB of RAM you've shown.
As to connecting to the internet, the motherboard has an ethernet port included and as long as you've got a broadband connection at home, you're set. Ethernet will be the safest and usually the fastest connection.
Hope this helps.
Grif

Chowhound
Comic Vine
GameFAQs
GameSpot
Giant Bomb
TechRepublic