OP, Your presenting a situation that is not really possible. You want to spend no more than $50, but you also want to run Minecraft on very high settings. Sorry, but there's just nothing out there that can do what you want.
If you absolutely refuse to go any higher than $50 (and can't wait for a rebate to get back to you), I'd probably recommend a GT 430. http://www.newegg.com/Product/Product.aspx?Item=N82E16814500263
... but if you get that I can't guarantee you'll be able to run your game on highest settings (I've never played Minecraft).
Otherwise, I'd echo what the guy a couple posts above me just said. Get a 6670. There are a couple on Newegg with $15 and $20 rebates that will bring the total cost to $50. If you want a marked improvement in performance then taking the couple extra dollars and waiting for your rebate is HIGHLY recommended. You're simply not going to get a card any nicer than that for less. There's likely a very noticeable difference between the 6670 and anything cheaper. They are one of the best "cheap" value cards out there.
Here are the 6670 links:http://www.newegg.com/Product/Product.aspx?Item=N82E16814102988http://www.newegg.com/Product/Product.aspx?Item=N82E16814125403
Edit: In addition, as someone just noted, you may need to upgrade power supply if you don't have enough wattage. Check that before buying anything. Getting improved video card performance is not a cheap venture.