The CPU is ok but you have no video card there only a dedicated NVidia GeForce 6150 LE video card (with 128 MB of dedicated video memory). If you will install one it will probably void your warranty if the "box" is sealed.
There is no problem with stability if you overclock it right.
For what it has i would not bother trying to overclock. There is no reason to do so.
Also for a new video card you will probably need a new power supply. ( link to the PC specks: http://www.nextag.com/HP-Pavilion-M8200N-Desktop-561703861/specs-html
Just use it as it is. Enjoy the PC at it's speeds.
In the future you should consider getting a PC made from parts. For that you will have to know what you are doing or ask someone. Or even better come back here on the forums and ask the community because there are so many people here that can help you make a good PC for your money.
If you received that PC as a gift, have fun with it:).
PS: if you want to invest some more and upgrade it let us know.