It certainly doesn't hurt to upgrade anyway--especially now.  Computer stuff is getting so cheap.
You can get get a Direct X 10 capable card with 512mb of ram for about $100, depending on your slot
 (although from what I've read it won't improve the graphics on the Sims 2 over 9.0C because the game was not designed to exploit the new capabilities--but other games do).

According to the web site, your card should be compatable.  The thing that may be getting you into trouble is the Direct X.  Apartment life requires 9.0c  the radeon 9250 is Direct X 8.1.

If the rumor mentioned in this thread about Sims 3 being DirectX 10, then it is going to be expensive for me.  DirectX 10 is being billed as only useable with Windows Vista (which I have resisted buying because of poor word-of-mouth).  This basically means before I can play it on my computer, I will have to buy:

--MS Vista ($100)
--New video card for DX10 (>$100)
--New mother board, because DX 10 cards mostly us the new PCI-E slot (>$80)
--New power supply, because new video cards suck up a lot of power ($40)

In short, I could buy a bare-bones computer for less.  And that doesn't even take into consideration the cost of the game.

This sort of indirect cost would certainly cause me to think twice about buying the game.