There are some skills that basically every player will want to train because they’re useful no matter what ship you’re flying.
Hull Upgrades Level IV allows you to use the better Damage Control II
module, which is a significant improvement over the basic version of the module,
making your ship more survivable.
Shield Upgrades Level IV allows you to use better shield-related modules, improving
your shield-based defenses. (Caldari, Gallente, and Minmatar only. If you’re
using ships that focus on armor defenses, you can skip this for now.)
Energy Grid Upgrades Level III allows you to use a lot of new capacitor-related
modules, making it easier to create ship fits that don’t run out of capacitor
quite as easily. Level IV lets you upgrade many of those modules to their better
tech 2 variants, further improving capacitor benefits. You’ll definitely want to
train III, and eventually you’ll want to train IV, too.
If the ships you’re flying have drone bays, Drones Level III and
Light Drone Operation Level I are highly recommended so that your ships
can use at least light combat drones, which provide some additional combat
capability for any ship with a drone bay. If you decide to keep using
drones you’ll eventually want to train Drones Level V so that you
can launch up to 5 drones (assuming the ship allows it).