what is the best method to reboot F5 LTm

Before rebooting your BIG-IP please make sure you can control the boot process from CLI by attaching a serial console (never ever change it from the defaults 19.200 8N1 settings) allowing you to select the boot volume of your choice.

In case you do not have a serial console you may consider to monitor the boot process via SSH connection to the AOM (Always On Module).

For unattended reboots please make sure in advance you are booting into the right boot volume by running:

switchboot -l

It will list the available and default boot volume of your system.

For a pure reboot the following command from CLI will do the job:

shutdown -r now

If you use the "-h" switch, the unit will halt and you need to power it on via AOM/SCCP (serial or SSH connection required) or by pushing a button on the appliance front panel (might be a challenge with device in remote location!).

A reboot may be followed by file system checks (and depending on upgrade / downgrade operations changes to BIOS, MOS, build-in FPGA followed by additional automated reboots.)

Be very careful if your command prompt contains exclamation marks ("!"). Upgrades to components may still be in progress.

After a reboot I used to monitor the /var/log/ltm ("tail -f /var/log/ltm") to check everything is finished before applying new changes to the system.