I have and use the heck out of this set: Lee Valley Brad Point Bits. Yes, they're twice the price of the OP's preferred price, but they're the best bradpoints I've ever used. I've even got multiples of some of most commonly used sizes as backups. You could always get a smaller set of them, then add bits as you need the sizes. I made due with a 7 piece set of bradpoints for years, and probably still could if I stuck to more common sizes of hardware and such.
I have an older set of TiN coated bit form Northern Tool. I've had them since '98 or '99. I've used fair number of them, but nowhere near even half the sizes. They work okay, but not great. I found that I needed to sharpen most of them to get good results, even the brand new, unused bits.
As a side note, I still have a set my dad got me from Sears for my 12th birthday (31 years ago). I've lost a couple bits, but I still use them and they still cut fantastically, even in steel. Those I've never resharpened, though it'd be interesting to see how they perform with new edges.