If you look into industrial robot arm design, you'll see that three different power options are typically used (in order of descreasing power): Hydraulic, Pneumatic, and Electric.
There are, though, a few industrial robot designs that use electric, and are quite fast, and very powerful. Typically, these designs use really large motors, as well as coreless motor designs. You'll also see designs where the motor is incorporated into the joint (typically, these motors too will be coreless, and/or they will be pancake style); incorporating the motor as an integral part of the joint (so the joint forms the case and bearing supports) makes for a lighter motor, and thus a lighter arm, but keeps the torque up.
Even so - if you look at what the arm in total weighs, and how much the end-effector can lift, you'll see it is quite low in comparison. I once found an old used Unimate at a local surplus yard (Equipment Exchange here in Phoenix), and was surprised at its size (total length of base and arm together were about the same size as my Ford Ranger I was driving at the time). This was a hydraulic arm, and weighed quite a lot - but the end-effector lift weight wasn't really large.
So - do whatever you can to minimize the total arm weight while maximizing its strength. Keep the motors as close to the base as possible (look at old trainer robots like the Armdroid for ideas; you might also look at the Unimate Puma for some ideas as well). Use lightweight but strong materials for the arm (alluminum space frame?). Use larger and stronger motors for the joints as they approach the base (that is, the shoulder rotation and pitch motors should be -really- hefty, whereas the elbow motor(s) can be lighter, the wrist motors lighter still, and the gripper motor lightest of all). Reduce friction as much as possible (friction wastes torque that could go toward lifting the arm and payload).
There are several books out there on industrial robot arm design (and control); you should try to find some copies of them...