Gaming Video Card needed for a slim Dell 531s case?

Because the Inspiron 531s has a weak (and proprietary) 250W power supply, that restricts your upgrade options. The best card that's guaranteed to work in your computer is a Radeon HD 6450, which isn't very powerful, but still way better than your built-in graphics:

http://www.newegg.com/Product/Product.aspx?Item=N8...

What you really want is a Radeon HD 6570, which is just barely slower than a GeForce 8800GT. It offers the best bang/buck at $60.

http://www.newegg.com/Product/Product.aspx?Item=N8...

There's only one low-profile graphics card faster than a GeForce 8800GT. That's the Radeon HD 6670, but it's considerably more expensive than the 6570.

http://www.newegg.com/Product/Product.aspx?Item=N8...

http://www.newegg.com/Product/Product.aspx?Item=N8...

The problem- you'll most likely need a 300W or higher power supply to successfully run either of the 6570 or 6670. The official manufacturers recommendation of 400W is overinflated, but anything below 300W is probably a no-go. Some people have reported success installing the 6570 in slimline computers with 250W power supplies, so you might give that a try. But to be safe, you'd need to upgrade the PSU.

The good news is that stronger power supplies DO exist for that particular slimline model- but of course a PSU upgrade raises your upgrade cost.

http://www.ebay.com/itm/320636663425

For almost all low-profile cards, the VGA port is lost when you attach the low-profile bracket. You'll have to use a DVI->VGA adapter. Note the pictures of the cards linked above.

Graphics card performance and hierarchy chart- for reference the Radeon HD 6570 is about 3fp slower than the 5670:

http://www.techpowerup.com/reviews/Zotac/GeForce_G...

http://www.tomshardware.co.uk/gaming-graphics-card...