I hate to ask, but a drill bit spinning on top of a wooden stud sounds like the drill is running the wrong direction or the bit is just plain worn out. I don't mean to sound remedial, but from the user end of the drill, as you would be holding the drill motor, the chuck should be turning clockwise. Or if you are staring down the cutting tip it should spin counter-clockwise. Just covering the basics...
High Speed Steel (HSS): Most any black colored drill is going to be (Black Oxide Coated) or (Blued) HSS and they are good for most anything. The silver colored ones are HSS without the black oxide/blued coating. The sharpened end is heat treated hard and the shank is softer to absorb mechanical shocking.
Titanium Oxide Coated Drill Bits: They are HSS with a coating to increase the durability or make them wear longer.
Cobalt Steel Drill Bits: They are used to drill hardened steel for stainless steel which has a higher degree of difficulty of machining. They are usually a different color, kind of a warm brown color and the very end of the shank is turned down or a smaller diameter to identify them.
Carbide Tipped Drill Bits are used for Concrete and Glass. The shank is HSS and they have carbide inserts soldered or welded to the tip.
Most any commercial drill bit will be good, but they don't last forever. Stay away from Harbor Freight Drill Bits because there is no telling how good they are and HF seems to me to be very inconsistent from day to day. Try a local tool supplier or even sears. Check the two below. They are factional only and will serve most home owners.
Black Oxide Fractional Set: $69.99
http://www.craftsman.com/shc/s/p_10155_12602_00964083000P?vName=Tools+&+Equipment&keyword=drill+bit
Titanium Oxide Fractional Set: $99.99
http://www.craftsman.com/shc/s/p_10155_12602_00964073000P?vName=Tools+&+Equipment&keyword=drill+bit
Bigger sets are available at many locations on the web. If I were you I would stay close to the industry type suppliers like MSC.com or Mcmaster.com
http://www1.mscdirect.com/CGI/GSDRVSM?PMTYPE=&SITEXT=DRILL SETS
http://www.mcmaster.com/
You will most likely use what is called "Jobber Length" and 135 degree angle tip which is good for most home owner stuff. Other options for harder materials are 118 degree.
For $250 you can get a full set of 1/16" to 1/2" x 64ths, A to Z, 1 to 60.
Price is the real key here...