You do not "need" to softmod your friend's console unless you specifically don't want to modchip it... What equipment you need depends on how you choose to go about it.
For example, if you're prepared to transfer that modchip, then yes, that'd be a good way to do it. Shove the chip in, and assuming the BIOS it's using is compatible with that machine (check your
machine versions first), it'll accept the new HDD right off the bat (same as your console would). You can then boot off something like Auto Installer Deluxe (AID) or HeXEn, format the drive, install a softmod and a dashboard, lock the drive (ConfigMagic can do this for you), then finally remove the modchip. Extracting the EEPROM is unnecessary if using a modchip, but it's still a good idea to take a backup.
Don't worry about TSOP flashing until the machine is softmodded. You can't do it until then. However, yes, the
results are very nearly the same as those you'd get from permanently installing a modchip in the console.
(A modchip, when turned on, overrides the BIOS on the console's motherboard. Flashing the TSOP completely
replaces the BIOS on the motherboard instead. Only pre-1.6 consoles have flashable TSOP chips).