Ask a dozen strength coaches what the best overall triceps-builder is and most will say either the close-grip bench press or dips. These are compound movements that allow you to create the greatest overload of the triceps. They also involve other muscle groups (pecs and delts) but they're still considered the best way to start a triceps workout.
Think of all the main muscles in your body and the big lifts you'd do to hit them: pecs, lats, quads, hams, triceps, delts, etc. They all have their own compound movement or bread-and-butter lift.
For pecs the bench press (or dips), for delts the military press, for quads the squat, for hamstrings the Romanian deadlift, and for the upper back it'd be either barbell rows or pull-ups.
But for biceps, it's weird. When we think of its bread-and-butter lift, the first thing that comes to mind is the standing barbell curl.
Listen, there's a multi-joint big basic for the biceps too: the supinated (palms facing you) close-grip pull-up. That exercise shows greater biceps activation than most direct biceps exercises while also using a heavier load. Keep in mind, you're lifting around 97% of your bodyweight with no added weight, and it's even more effective if you DO add weight.
If you want to build your biceps, start your workout with the close-grip supinated chin-up. Load it up pretty heavy so that you reps will fall in the 6-10 range. Your goal should be to get stronger in that range while maintaining proper form.
But what if you can't even do 6 proper chin-ups with bodyweight?
You have two main options:
1. Use a partial range of motion.
Start from the bottom and pull yourself up as high as possible (without cheating or contorting). Over time, your goal will be to get higher and higher.
2. Use a lat pulldown.
If you can't even do a partial rep, use a close-grip, supinated lat pulldown. To make it work you must have the impression of pulling it down toward you, not simply down.
This should be the first exercise when training biceps. Don't go to failure, since chin-ups respond well to the greasing-the-groove approach of daily practice.