You can do some serious damage with $300. Here are the top 2 choices I would pick.
$279.99-EVGA 896-P3-1260-AR GeForce GTX 260 896MB 448-bit GDDR3 PCI Express 2.0 x16 HDCP Ready SLI Supported Video Card - Retail
http://www.newegg.com/Product/Produc...82E16814130370
$284.99-SAPPHIRE 100243L Radeon HD 4870 512MB 256-bit GDDR5 PCI Express 2.0 x16 HDCP Ready CrossFire Supported Video Card - Retail
http://www.newegg.com/Product/Produc...82E16814102748
As far as pure processing and rendering power, the ATI card is probably stronger. But the Nvidia card has more ram, which means it may run smoother on your larger monitor at higher resolutions. I should probably note right now that the larger monitors require more ram because of the higher resolutions that they run at, especially if you are running with antialiasing on.
However, I mentioned before that I am Nvidia biased. And I am. So I would probably still get the GTX 260 (GT200 is the GPU). More ram, free shipping so I think it comes out to be alittle bit cheaper, and I think that Nvidia has better drivers. Before my current system I was running a Radeon 9800XT 256MB. It was a great card, bested Nvidia at the time I bought it. But the Catalyst drivers were flakey sometimes, mind you that was a 5 year old card when I replaced it finally.
I'll post up a few good cheaper options, but really go with your gut. Whatever you feel happy and pleased with is what you'll enjoy the most.