No need to change out the motherboard unless you plan to overclock. And the eMachine chassis is actually pretty nice for a pre-built.
The PSU definitely needs upgrading, and the graphics card is surely needed. The RAM is one that can be upgraded but wouldn't kill it if it wasn't.
Oh, you may want to toss in a case fan for the rear of the computer. When I added one to my eMachine is dropped the temp by 6-8 degrees.