I dont know my butt from my elbow
 

Im a young 16 year old man. Looking to find a lathe to hold 5mm pieces of cut round 1/4" stock. The stock will be cut to 5mm or roughly 0.197 inches (i dont have my calculator handy so i cant express that as a fraction-simplified). It has to be able to drill a 1/16" hole through the center of the stock. and then countersink that with a 3/16" hole. The stock will range from aluminum, acrylic, or urethane. Could anybody direct me to the type of lathe' i will need to complete this job? I need something very small and as cheap as it can come.

I'd look at one of the mini-lathes.