Yes, upgraded C + LB & SS = Hydra's replacement.
However, if you didn't want to waste time or money acquiring Handgun bullets, having the Hydra and Griffon around was pretty useful. I didn't know about the Model Gun until after I'd finished the game and played through again. I still haven't made enough money to upgrade to the Ultima Weapon.
Ice Magic = homing
Blizzard was useful when fighting enemies from afar. You could get the same effects from Vincent's Galian Beast transformation, but if you didn't have any Limit Breakers and didn't want to waste time finding your enemy through the Sight Scope or blasting away at them until you finally dropped them . . . then Blizzard would be for you.
Fire Magic = range
I personally didn't like Fire all that much. Judging by the radius, you could shoot a single soldier and miss his entourage coming up from behind. However, it was pretty useful against enemies who seemed to group together.
Thunder Magic = group
Unlike Fire, Thunder chains to enemies who are a particular distance from each other. Sometimes, there may be some missed stragglers and Thunder does less damage than Fire or Blizzard, but will certainly knock a huge group down, even if they aren't that close together.
Melee was only useful when you rarely felt like saving ammo.