Well, when you say a $75 case/power supply combo is stretching the budget, you really are limiting your options. I'm not crazy about this one, but it should suit your needs:http://www.newegg.com/Product/Product.aspx?Item=N82E16811190105
My real recommendation, however is to increase the budget. Get an HTPC case that:
1) is full height (so you're not limited to low-profile cards and has better cooling)
2) has at least two internal 3.5: HDD bays (two if they're separated, three if all together), and
3) is aesthetically pleasing to you.
You would also get a decent power supply from Antec, Corsair, Seasonic, PC Power and Cooling, etc...