The only issue with putting a new card and psu into an emachine is if you have a case that isn't big enough to fit the psu or card or if you motherboard lacks a PCIe slot. Other than that it should be fine. I'd check your dimensions to be sure.
The Motherboard DOES have a PCI-E 2.0 x16 Slot and the case looks like it should have enough space for that PSU. You shouldn't have issues. Your processor and Memory will be SERIOUS bottlenecks though.