you are correct with the push/pull terminology. Pull-pull is most common. Any string that does not stretch much can be used. Fishing leader line, kevlar thread, etc. The hobby shops sell kits that include the string and some rigging for the ends.

The best setup for two elevator servos is that both elevator halves operate independently -- that is, they are not physically connected. Use a reversing "Y" cable from your receiver to the servos. If both servos are more or less the same, both elevator halves will go up and down about the same amount. If you have a fancy radio you can plug one elevator into a separate channel (e.g. AUX2) and mix 100% of elevator into AUX2. If one half goes up when the other half goes down, then change the mix to minus-100%. On most planes it really doesn't matter if one half goes up or down a little more than the other half. Also, depending upon the transmitter, the elevator trim tab on the transmitter face may only affect one of the elevator halves. Again, for most sport planes, this is not a problem.