What is the best possible Video Card I could run?
Since you're looking at upgrading a pre-built machine, you're going to have to do a little homework. Many Dell machines (outside of their high end gaming setups) ship with proprietary parts, and off-the-shelf parts aren't always compatible. The power connector on the motherboard may be keyed differently, for example, which means you could purchase a new PSU and it might not work. It might not even fit in the case.
As to your videocard, you first have to figure out what interface it uses. From a cursory glance at Google, it looks like the Dimension 4700 comes with a PCI-E based foundation, which is good, but you'll want to verify this. If that's the case, the fastest videocard out there right now is Nvidia's dual-GPU GTX 295. The fastest single-GPU card is ATI's HD 5870. And the smarter money is on less expensive cards that pack a punch, like the GTX 275, for example.
But before you go out and buy a card, find out if you can swap in an aftermarket PSU in your system, and make sure your case has room to accommodate a two-slot videocard (most videocards take up two slots).
Finally, I'd suggest opening a thread in this same forum (Help Me Buy/Help Me Build) for help on your upgrade.