If you are talking about a 35mm film camera, the 85mm is good for head and shoulder portraits. You can fill the frame with their face, but that's starts getting a little close. The 60mm would be out for strict portraits. On a 1.5 or 1.6 crop digital SLR, the 60mm would give you the same field of view as a 80mm or 85mm lens on a film camera, so the same thing applies as the 85mm. The 85mm would be around 130mm, which is on the other end of a typical portrait lens. It would be great for head shots, and you could just back up for head/shoulder shots.
What camera are you using now? Do you have a zoom? Just set it to the focal lengths you want to try out.