The GeForce GTX 660 seems like a pretty good deal, and a lot of the cards that fit most of my criteria on eBay are around the $200 range.
Now I have a follow-up question for anyone with some input:
Are there any manufacturers I should go for or avoid? Years ago I had a BFG card that was pretty good; my last card was a PNY that I was never that happy with. It was just alright, but the fan made noise and eventually broke down. The card I am using now is an EVGA, which has a Geforce GT 610. Not very good, but I needed a cheap card as a stop-gap because I need my computer for my occupation. It's actually pretty good with games, but when it comes to rendering video with Nuke, it's a piece of trash. Well, maybe not trash, but it takes longer than it really should to render out a video that's just a few minutes long.
EDIT: Also, what about Zotac? I came across a few of those on eBay and I'm wondering if anyone here has experience with that manufacturer.