Crucial guarantees compatible RAM for name brand systems. Here is the link for your system: http://www.crucial.com/store/listpar...Dimension+5150
I would get at least another 512MB.
According to Dell, your system is a Dimension 5150. (The DM051 is the BIOS string ID). And according to the 5150's technical specs, you have a free PCI-Express slot and a 305W power supply. Unfortunately 305w doesn't give you too much head room for a very powerful video card, but Dell power supplies are usually high quality, so you can still get one. (Dell's spec link for anyone interested: http://support.dell.com/support/edoc....htm#wp1052310
I don't know your budget, but I'll keep it low. Take a look at this card:
Radeon X1300Pro: http://www.newegg.com/Product/Produc...82E16814127193