Hey, welcome to a great game and hope you like challenges!
I also have a caldari character and although missiles do not do the greatest damage you do not have to worry about falloffs, optimals and can choose your damage types (i.e. kinetic, em, thermal or explosive)
To answer your question...
Frigate - Kestrel, by far one of the coolest frigates to fly. They can be hard on your powergrid but do a decent amount of damage for a frigate while remaining out of range of your enemy.
Cruiser - Caracal - this ship is all about the missiles and will provide you with a nice range on your targets since you get a bonus to missile velocity
Battle cruiser - Drake - this ship can fit 7 heavy launchers and passive tank level 4's with ease. One of my favorite ships in the game
Battleship - Raven and scorp both have launcher hardpoints, however the Scorpion is more for EWAR or a support role so the highs sometimes get used for reps or neutralizers.
Other Caldari missile boats:
Cerberus - tech II Heavy assault cruiser (HAC)
Onyx - tech II heavy interdictor cruiser (HIC)
Fly Catcher - tech II interdictor (DIC)
Manticore - Tech II stealth bomber
Golem - tech II marauder
Now as to which order... if you want to mission go kestrel for lvl 1's, caracal for lvl 2's, drake for 3's and easy 4's then raven for hard 4's
If you are looking for some more advice in-game or people to play with check out the corporation
they are a cool bunch of guys to learn the game from.
Hope this helped!
past EVE-online experience