Everyone's offered decent suggestions... However... For my money, I prefer the 17" widescreen laptops. You get a huge screen for anime/dvd's/gaming/etc. as well as a full number pad. And for FFXI... I <3 the number pad.
I bought a Toshiba Satellite 17" a couple of years ago and it can still run 2 windows of FFXI Windower pretty smoothly.
Toshiba has the Satellite and Qosmio lines that both come in 17"+.
They're a "little" out of your $500 price range, but you're looking at 800-1000 if you want a decent laptop tbh.
You're looking at $500-600 minimum if you get a 17" Toshiba with integrated video. You can then customize the models from there on their site or buy from a dealer.
MicroCenter has some GREAT deals on practically anything computer/tech related. Right now they have a big sale on laptops too.
$650 Toshiba Satellite P305D-S8900# AMD® Turion 64 X2 Dual-Core Mobile Processor RM-70
# 4GB DDR2-800 RAM
# 320GB 5,400RPM Hard Drive
# Labelflash SuperMulti Double Layer DVD±RW Drive
# 5-in-1 Bridge Media Adapter
# ATI Radeon 3100
# 10/100 Network
# Atheros® 802.11b/g/n Wireless Network
# 17.1" Widescreen XGA+ TruBrite Display
# Microsoft Windows Vista Home Premium (64-bit)
And here's a link to all of their laptops on sale.
http://www.microcenter.com/search/search_results.phtml?coordinate_group=ED1B+ED1D+ED1F+ED1H&feature=058339&utm_source=mcol&utm_medium=leader_bnr&utm_campaign=hmpg_ntbks061509