There are AGP cards out there if you search places like Amazon. (Though the price for the performance doesn't get as good as the PCI-e cards.)
PCI-e is newer and PCI-e cards will not work on AGP or normal PCI slots and require motherboards that have available PCI-e slots. The fact that you have an AGP slot is a dead giveaway your computer is old and it may just be time to buy a new one.
Still, AGP cards are still for sale.
Here's one.
http://www.amazon.com/AMD-ATI-Radeon-X1300-Card/dp/B000E5VQP4/ref=sr_1_6?ie=UTF8&qid=1315963007&sr=8-6
This one should have a much better chance in running the Sims 3, but ouch, it's expensive!
http://www.amazon.com/HIS-Radeon-Native-Graphics-H467QS1GHA/dp/B003CYKCG8/ref=sr_1_5?ie=UTF8&qid=1315963007&sr=8-5
- Edit -
If you have an AGP slot, it's a dead giveaway that you cant use ant PCI-e cards.
Try restarting your computer and pressing 'delete' during the BIOS load up. Hopefully from here you can find out your motherboards brand name. After writing it down, google it in order to find out it's specifications-- you should be able to figure out what types the slot are.