If you carry the power, then you're likely to want LiPo batteries, as they have the highest power to weight ratio. LiFePO4 batteries come second, and have a much longer lifetime, so if this is something you have in service every day, that might be a more economical choice.
Servos: For a bot as big as 50 cm across, I would recommend Dynamixel MX-64 servos. They have the best torque-to-price ratio in that class. The MX-28 are somewhat cheaper, but have significantly less torque. The MX-106 are somewhat more powerful, but a lot more expensive. The cheaper AX series is likely not powerful enough to support that large a span (although you might be able to do something with the AX-18 -- could be worth running the numbers on that.)
An alternative might be the Herkulex DRS-0201 servos. Again, run the numbers on those before you commit, because they may not be sufficient for your load. Also note that any servo of any brand should be designed to carry 1/4 or less of the rated stall torque in "normal" situations, which in the case of a hexapod means 3 legs on the ground.