The RAM and HDD that could help a lot.
http://www.cnet.com/products/dell-inspiron-3847-core-i3-4130-3-4-ghz-4-gb-1-tb/specs/ has the basic intel.
"One (1) PCI Express x16 slot; Two (2) PCI Express x1 slot" seems to be inside.
Since you are not changing the PSU you won't be putting a gaming card in there. I suggest you max out the RAM until you can get over the PSU hurdle.
Bob
I5, 8gb, with integrated Intel HD Graphics 4400 Dynamic Video Memory Technology. What card would be a decent upgrade for better gaming and dealing with large graphic files. I would also like to keep the current power supply, 300W I believe.

Chowhound
Comic Vine
GameFAQs
GameSpot
Giant Bomb
TechRepublic