Video card for the gateway 507gr

The 507GR had onboard video - so when you insert a new card you will have to deactivate the onboard video in Device Manager.

As regards the replacement card - any modern card will work fine, what you need to know though is whether your motherboard has an AGP riser or will accept PCI cards.

I have been told that PCI Express graphics cards are preferred over AGP cards, but I don't know why.

Good luck.

Yes, your computer specifically supports:

PCI Express 16x and
PCI Express 1x

The 16x is the long one and the 1x is the reallly short one. Most likely the card that you get will fit the big slot. Be careful not to upgrade too high though, because if you do you may have to upgrade your power supply as well. Ask someone at gateway or a local shop for a recommended card for your system.