I have that exact 256 MB GeForce 5500 FX, 'cept it was from XFX so your mileage may vary. The good news...I can run WoW at 1280x1024 with everything on max minus antialiasing, anitroscopic filtering, and full-screen glow at a decent FPS. The FPS gets a bit better if I shut down every background process and change WoW's priority to Very High. It's not 60 FPS silky-smooth but it's quite palatable. The bad news...it may be great with WoW but with any game released after Half-Life 2, it's pretty much crap. Works great with HL2 and other Source titles but anything after that, like F.E.A.R. and Oblivion, barely even run. I'm not sure why this gulf is so big - anything released in 2004 or earlier can run great on max settings, yet anything 2005 and beyond runs at 3 FPS. Anyway, I'm no expert but I do know it'll handle WoW just fine. If you're strapped for cash and if WoW is your main priority, that GeForce will handle it just fine. At this point in time, it will be little more than a stopgap so you can handle WoW, though. Expect to need to upgrade it sometime soon.
As for RAM, I'd say 512 is minimum. You'll still get long periods of lag-stutters in crowded cities and your gryphon flights will be choppy and unenjoyable, but aside from that you'll be good. Still, I found this annoying and went up to a gig. Instant difference! I've had games where upgrading RAM did diddly to fix the dismal performance, but it really matters in WoW. I no longer get ANY loading lag! Nowhere! Not even in Orgrimmar or Ironforge, or in raids. My gryph flights no longer lag or freeze up the image. My framerate does still go down a bit when my gryph flies over dense trees, but that's because of the video card.
If you're strapped for cash, I would suggest getting at least a GeForce FX card and 512 MB RAM. You can probably run WoW on borderline mid-high settings, or high with some tweaking plus an upgrade to 1 GB of RAM. I know zero about that other card so find someone else's opinion on that one.