what is the best method to reboot F5 LTm

Your unit will be completely unavailable during the reboot cycle! And depending on hardware, software, configuration elements and required component updates it will take at least a couple of minutes to get it back in service. If your are running your system in production, make sure you have initiated a failover to the peer unit of your sync-failover device-group (assuming you are on v11) and the other unit is active and handles the traffic. Without redundancy your service(s) provided via BIG-IP will be completely offline during the reboot cycle. If you do a failover, please verify your peripheral components (routers, firewalls, servers) get their ARP cache updated (may change without mac-masquerading if a virtual address [for VIP, SNAT, NAT, floating Self IP] moves to the failover unit and the related gratuitous ARPs from the F5 device get lost for some reason).