Solution 1 won't help much since you'll still be limited to 100 Mbps unless the backup unit also has two NICs that are teamed (and even then it won't really be faster because you only copy to the backup unit). If you have a Gigabit network, then install a Gigabit NIC and make sure that both the server and the backup unit are connected at Gigabit speed.
If your network is limited to 100 Mbps, then a Fibre Channel HBA card is a good solution, but upgrading to Gigabit Ethernet probably would be less expensive. Can your backup unit be connected via Gigabit Ethernet and/or Fibre Channel? Solution 3 will work only if you also have a Fibre Channel HBA in the backup unit. Fibre Channel is much faster than Gigabit Ethernet, but it might not be faster than Gigabit Ethernet if the backup unit is not fast enough.