Skill Discussions

Not positive, but one of the reasons you might not have gotten replies up to now is that the "from L1 to L4" part is a bit confusing. Do you mean you want to avoid training any skills to L5 if possible? Well... there are some that absolutely must be to L5 ASAP, including CPU Management and PG Management and Drones, and some that are prerequisites for other things (learn to use the "show info" right-click option on lots and lots of ships, modules, and skills...

But.... here is a list of skills you should have to at least L4 as soon as you can instead, then... I've tried to order from most important to less important within each category, but YMMV... this is not meant to be the order to train things, just in order of category:

...

Armor (yes, even for a shield-tanking-only pilot):

Hull Upgrades
Mechanics

Drones (semi-optional, you are a Caldari pilot, after all...):

Drones
Light Drone Operation
Medium Drone Operation
Drone Interfacing
Drone Navigation

Electronic Systems (semi-optional):

Cloaking
Electronic Warfare
Propulsion Jamming
Target Painting

Engineering (must haves):

Capacitor Management
Capacitor Systems Operation
CPU Management
Power Grid Management
Weapon Upgrades
Electronics Upgrades
Energy Grid Upgrades

Gunnery (if you wanna do hybrids with your Caldari frigs/destroyers/cruisers such as Merlins, Cormorants, Moas):

Gunnery
Small Hybrid Turret
Medium Hybrid Turret
Sharpshooter
Motion Prediction
Rapid Firing
Controlled Bursts
Surgical Strike
Trajectory Analysis

Missiles (if you wanna do missiles with your Caldari frigs/destroyers/cruisers such as Kestrels, Coraxes, Caracals):

Missile Launcher Operation
Rockets
Light Missiles
Heavy Assault Missiles
Heavy Missiles
Missile Projection
Missile Bombardment
Rapid Launch
Target Navigation Prediction
Guided Missile Precision
Warhead Upgrades

Navigation (must haves, top = affects all ships, bottom = more specific to AB/MWD usage):

Navigation
Evasive Maneuvering
Warp Drive Operation
Afterburner
Acceleration Control
Fuel Conservation
High Speed Maneuvering

Neural Enhancement (optional):

Cybernetics
Biology
Infomorph Psychology
Infomorph Synchronizing

Rigging (optional):

Jury Rigging
Astronautics Rigging
Hybrid Weapon Rigging
Launcher Rigging
Shield Rigging

Science (optional... needed for Cybernetics/Biology above):

Science

Shields (absolutely essential!):

Shield Management
Shield Operation
Shield Upgrades
Shield Compensation
Tactical Shield Manipulation

Spaceship Command (pretty simple for you at first):

Spaceship Command
Caldari Frigate
Caldari Destroyer
Caldari Cruiser

Targeting:

Target Management
Signature Analysis
Long Range Targeting
Gravimetric Sensor Compensation

.... and there ya go. Those are the most important skills for a PVP-centric Caldari frigate/DD/cruiser pilot, IMO. HTH.

You're going to want drones above Destroyer with Caldari. Starting at cruisers, drones - will serve you extremely well as a necessary / non negotiable counter to frigates which get under your guns/missile explosion radius.

What I'd tell you, is that BC and below will use one size of weapons, and BS use another size.
The training time is not a trivial amount of time, and IMO it is better to have one GOOD set of weapons, over two half assed sets.

That said,
BS are better for level IV missions, hands down. If ISK is a thing you need to earn in game, take the fastest route to BS.

When in doubt, train ships and weapons skills. Skills that will help all size hulls will be the missile SUPORT skills (Caldari)
For most ships, the hull skill to V is absolutely worth the train.

I am doing Caldari and Gallente first because they use the same weapons systems. But I am not sure if I will stick to my plan and train small/medium missiles and hybrids to T2 first or "multiclass" to Amarr and Minmatar and get projectiles and lasers to skilevel 4.

I other games I prevered to master one thing before moving on, but EVE has massive dimishing returns and "all 4" is faster than "some 5".