I don't know about the angle of the bit cut, but I use the two sets below (both bought through Amazon). The Steelex Plus D1138 HSS Tin Dill set (left) is a great set, which I got on Amazon for around $55 meets all your criteria except the reduced 3/8 inch shank. With 115 bits it always has a size for everything from 1/16 to 1/2. I've used it to cut mild steel, wood , plastic, composites, etc. About $55. The wood case, about $37 normally, has five bits in each of 20 sizes from .3 mm to 1.6 mm, all suitable for a pin vise which I use for fine work. I've never used these on anything but wood or plastic.
I am a big believer in not buying expensive drill bits (or saw blades) or trying to resharpen old bits (my experience is they walk a lot more thereafter). I view them as disposeable units. I don't buy the cheapest, but these are examples of great value. I've never had one go dull but some of the small ones do break from time to time and I tend, despite taking some care, to lose the odd bit from time to time. So I just buy a new set when they are on sale about ever two years and chuck (pun intended) the old one (I recently got a new set of 115 pieces for $23!!) and just renew the entire set.
