How will this computer run games?

Your processor and RAM are more than capable of running Skyrim, and will do an exemplary job at running most newer games, as well. The only thing you'd want to look at improving is your GPU. There are a lot of quality desktop GPU upgrades you could go for at less than $300.

No problem! Glad I could help.

If it is possible in your budget, do you plan on upgrading your GPU? If you do, I could suggest some graphics cards that I think will work for you, within that budget. Cheers!

Your graphics card outclasses a GeForce GT 610, which I've had prior experience with. You should get a playable frame rate (around 30 FPS) with lowered graphic settings.

Just, like, turning down the detail of the textures and such in some games. For example: You'll run Minecraft with no problems, but with games like Chivalry: Medieval Warfare, you're going to need to drop down the quality of everything a bit.

Don't mention it. Have a good one.

I am sorry I must say you're wrong. A A8-6500 is a APU, APUs are made as contenders for tablets, notepads, and other 'light computing devices' by building the GPU INTO the CPU.

http://en.wikipedia.org/wiki/AMD_Accelerated_Processing_Unit

These newer APUs perform 'better' for old games like Tomb Raider, when compared to Intel Integrated Graphic, but that is a comparison in gaming terms like comparing which is faster a snail or a small turtle? Yeah one will be faster but really who cares when we are talking numbers like in Metro Last Light on LOW GRAPHICS (1280x800!!!) settings in the 30s and below?

http://www.xbitlabs.com/articles/cpu/display/amd-a10-a8-a6_7.html#sect0
http://www.legitreviews.com/amd-a10-6800k-and-a10-6700-richland-apu-reviews_2209/11
http://www.overclockers.com/amd-richland-a106800k-apu-review/

***NOTE: LOOK CAREFULLY at the numbers and details DO NOT BE FOOLED by the 'length of the line' as a measurement!****

Your APU will NOT be able to handle BF4, Ghosts and "Newer" games AT ALL. BF4 is VERY CPU intensive (for example), requiring real dedicated Quad Core CPU (minimum) then handed off to a dedicated GPU. A APU is compared to Integrated GPUs for a very good reason.

No aggression just pointing out that the incredibly LOW performance level when specifically said "how it will run some of the *Newer* games out there"
and you were getting VERY WRONG ADVISE

And yes IF you looked at the site
Metro: Last Light (2013) low: 33.8 fps <<< AS I SAID "we are talking numbers like in Metro Last Light...in the 30s and below"
Compare med.: 25.6 fps
Compare high: 12.5 fps
Compare ultra: 6.3 fps
» The benchmarks indicate that the game is not playable in the tested settings.

Assassin´s Creed IV: Black Flag (2013)
low: 34.8 fps
Compare med.: 25.4 fps
Compare high: 12.8 fps
Compare » The benchmarks indicate that the game is not playable in the tested settings.

Need for Speed: Rivals (2013): Not playable with a weaker graphics card. - more...

Battlefield 4Battlefield 4 (2013) low: 37 fps
Compare med.: 26.5 fps
Compare high: 17.8 fps
Compare ultra: 6.2 fps
Compare » With all tested laptops playable in detail settings low.

Batman: Arkham Origins (2013) low: 64 fps
Compare med.: 37 fps
Compare high: 21 fps
Compare ultra: 10 fps
Compare » With all tested laptops playable in detail settings med..

These ARE "*Newer* games out there". Bottom line: Your APU will be the bottleneck for all newer games, and any older games will be hit and miss, but performance will the SAME as a computer WITHOUT a GPU but using INTEGRATED graphics performance levels. If that is your goal/expectations, then your right on the mark, but for any games going forward you need to replace the computer (FYI if this is a OEM computer i.e. Dell, Gateway, etc., the Windows included is ONLY usable and will refuse to load on ANY other system if you try to 'move it' to a new build.).

What sorta one would you be looking at for about $300 or little less which are fairly good because I might get one sort off like this PC

What GPU & PSU would u put in? Budget in mind. And do i need to get more cooling for it then?

Nah, you don't have to get additional cooling. Get a Video card that has a fan on it, it should be more than enough. You'll need serious cooling if you overclock your processor and has SLI bridge or something for your GPU.

With your current spec, I think you need to tone down the game graphics, esp if you want to play skyrim. With your rig, you could run games like Kingdom of Amalur, Dragon Age, Dungeon Siege and Eclipse War without suffering too much FPS drop on a medium setting.