Gaming build suggestion?

Hi all, can you guys tell me what you think about my build?
First time making my cpu.
I've done some research already, and i am not really sure which motherboard/PSU/RAM to get.


Processor: AMD Phenom II X4 965 Black Edition
Motherboard: ASUS M4A89GTD PRO-USB3.0
GPU: Powercolour HD 5870 1GB DDR5
PSU: COSAIR HX650W
HDD: Samsung 1TB F3 HD103SJ RPM7200
RAM: Kingston HyperX DDR3 1600 OR G-skill RIPJAWS DDR3 1600.
DVD/CD Drive: Samsung SATA 22XDVDRW
Monitor: Acer G235H 23' FullHD
PC Case: Need some recommendation. (Mid range preferred, not too big.)

Anything that needs to be changed?

Initial build was an i-5 but it shoots a lil out of my budget, so i've decided to go for AMD instead.
So here are some questions that i want to ask.

1. Will the power supply be sufficient for the above specs?
2. Is my motherboard ok? or is there a cheaper one that would be sufficient for me?
3. What to get to allow my desktop have wireless connection? (I know it's possible with some wireless card or something like that)
4. If my budget allows, should i get a cooling fan? Heard that CoolerMaster HYPER 212 Plus is a pretty good choice.
5. Lastly, this build will be able to run most games at full settings in 1920x1280 without lag , right?

I am from Singapore and will be buying the parts from shop, and the price are pretty much similar compared with Newegg's. So you guys could show me links in newegg if any part needs to be changed.


Any feedbacks would be greatly appreciated.