generally speaking emachines are pieces of shit.
Figure out how much you want to spend or a frame rate you would consider acceptable. If you don't make some kind of limits in the beginning you could wind up spending way more than you should. High end computer parts becomes a game of diminishing returns on the bleeding edge of things.
To start with try adding some more ram and maybe upgrading the graphics card. You might even be able to replace the CPU.
Another route you can try is overclocking. This is where you increasing clock speeds in your computer by physically lowering the temperature (and thus resistance). This lowers the life span of components so I wouldn't try this on anything you highly value.
The clockspeed is measure of time it takes for a signal to complete a circuit around the CPU or whatever else you are overclocking. Conductors usually have a certain amount of resistance. This resistance is partly dependent on temperature. Lowering temperature lowers resistance. At certain temperatures conductors will loses all resistance and become superconductors and electrical signals will move at the speed of light though in your computer you don't want to try that.
In addition to conductors integrated circuits are packed full of semiconductor material, namely silicon and it's variations(p type, n-type). Lowering temperatures can cause a phase change of these semiconductors to become conductors in the same way that a conductor can become a superconductor. You don't want that to happen.
Overclockers can relatively safely reach 2 to 3 time spec performances with a wide variety of machines. Usually the focus is on the CPU but RAM and the graphics card are often overclocked as well.
It will require a little bit of knowledge of refrigeration systems and other things but it is often cheaper than upgrading. If these components wouldn't have been used otherwise than there is no reason to worry about a little excess wear and tear