It depends on what make/model servo you use, but most servos run between $6.00 (USD) to $60.00 (USD).. It's dependent on size, torque, sleeve or ball-bearing. I've used mostly Futaba S3004 for most of my projects.. Ball-bearing support of the shaft, the drive gear is easy to modify to convert from 180-degree to constant (full) rotation. (grinding down the stop tab, removing the 10K POT from the underside, and replacing the POT off the circuitboard, with a mini POT that could be trimmed through a hole through the case.) Ran roughly $15.00 (USD) from a local hobby store.
the frame/claw of your arm could be metal (milled parts or sheet metal) or wood (milled or cut).. As the above video showed, even Popsicle sticks work.
Also, watch what the load is on the arm joints. (shoulder, elbow wrist.) If the load weight is too heavy, even gear driven, most servos do have some give, and will back-roll or possibly even break.