Trunk & Tag - YES; everywhere you can as long as it fits your security model.
LACP/PAgP - YES, use LACP (you can't use PAgP since it is Cisco proprietary).
Speed/Duplex - Autonegotiate; as a rule I always autonegotiate if it is 1000mb.
As for the config on your Cisco switch, it should look something like this with most of the config taking place on the port-channel and not the individual interfaces:
interface Port-channel1
description BigIP1
switchport
switchport trunk encapsulation dot1q
switchport trunk native vlan 999
switchport mode trunk
switchport nonegotiate