IMO, it would be best to swap out the Phenom for a i3-2100 - how set on AMD are you? Also, I'm not to familiar with Runescape, how intense is it graphically? You may be better off with a better GPU especially at 1080P if you go that route. Either way though, you could drop down to a smaller PSU such as the Antec TP550 New. On the other hand, if you prefer the AMD build, I would suggest the 955 instead to save a few bucks. Pair it with a newer 800 series mobo - the 880G has integrated graphics if it turns out Runescape is light on the GPU.
I also recommend getting an i3-2100. It's just as fast as the Phenom II x4 965BE and will consume much less power. It will also give you a solid upgrade path for your CPU in the future.
Also, the integrated graphics may be able to handle runescape, so you might not even need a dedicated GPU. If you do decide to get a dedicated GPU, I wouldn't recommend the GT 430. I would at least get a a Radeon HD 5570, if not a 5670.
Even though the i3 is dual core it's still faster than the AMD one? For my needs do i only need dual core? Will i be able to have runescape, youtube, and a couple of internet browers open without lagging? I like AMD because i'm using it right now, and i've had this computer for 4 or 5 years still works fine. But if the i3 is good i don't mind getting it.
^+1 to amk's suggestions.
Yes, it very consistently outperforms the Phenoms. It does have hyperthreading so that helps it out with more threaded workloads. Yes, the processor will not be your bottleneck either way.