There are four roles, or skill trees, you can spend experience on in Payday 2: the Mastermind, the Enforcer, the Technician, and the Ghost. Focusing on a particular role is great for specific play styles, but there are plenty of skills that can be mixed and matched among the four trees. Here are a few key skills you'll want to unlock.
Unlocking the Mastermind and Enforcer skill trees unlocks the Doctor Bag and Ammo Bag, respectively. You'll want these for every job, period - having a spot to replenish ammo and patch yourself up is a must. These are especially useful when camping out during a police assault.
In the Mastermind skill tree, you'll want to unlock the Fast Learner, Black Marketeer, and Endurance skills. Unlocking Fast Leaner grants you extra experience with every job, great for leveling up. Black Marketeer decreases the cost of items, which is just good business sense, and Endurance will increase your stamina.
In the Enforcer tree, you'll want to purchase the Transporter perk. This is essential for daisy chaining bags. Unlocking the skill allows you to carry them faster, and acing the skill greatly increases the distance you can throw them.
The Fast Hands skill, found on the Ghost skill tree, is also quite "handy" (please don't hold that joke against us). It allows you to pack loot faster, essential for any smash-and-grab job.