The human hand is much more diverse and complex than we often give it credit for and that means that lifters have a huge opportunity to specialize in individual aspects of grip strength. But it also means that not every grip related activity might carry over to your sport the way you think. The needs of an arm wrestler are going to vary from the needs of a competitive strongman. Both of those are going to be very different than the training of a martial artist or a rock climber.
Most gym rats want to train their grip for aesthetic reasons (as in they want to look like a Renaissance Fair sized turkey leg is hanging from their elbow) or because they want to be able to hold on to a loaded barbell long enough to get a down command.
Thick forearms are going to come primarily from wrist flexion and extension and, for that, you aren’t going to do much better than traditional wrist curls or a makeshift wrist roller. No need for extra bells and whistles here: just do a lot of reps of flexion and extension with your wrist under a load and your forearms will grow (though this is a pretty heavy duty option, if you’re in the market).
The ability to hold onto weight is going to come primarily from supporting strength. That’s the isometric strength that your fingers hand and wrist have that allow you to hold on to something for an extended period of time. Training for that is pretty different than training to actually crush something the way you would with something like the Captains of Crush hand grippers.
The best recipe to be able to hold onto barbells, thick or small, is to do any variation of timed holds. Farmer walks are great and they don’t have to be done with actual handles. Most people sleep on long holds that go a minute or longer and most people are going to find that a long carry with a pair of 80 lb dumbbells is going to get them right to this point. You can also do hangs from pull up bars or you can do timed holds in a rack. There are plenty of options but you aren’t better off for getting fancy.
If you do want to add some extra work via grippers, timed holds will help supporting strength exponentially more than actual reps. The Ironmind silver bullet is a cool way of training this; pinch the bullet with the end of the gripper and hold it out in front of you until it drops.
The biggest trick from Old-Timers is to just ditch the straps on your accessory work. This is something I get a lot of questions on and my basic advice is to use straps on the on the heaviest rows and deadlifts, the ones where performance will be limited by your grip, and then leave them off on all of the warm-up and back off sets.
Don’t obsess over going strapless: you will do more damage to your hams, glutes, midsection and back (by continuously having your grip be the weak link on those working sets) than you will help your grip. The hands can actually overtrain pretty quickly, so going through repeated sets where the bar is sliding out of you hands, threatening to shave your callouses off like a cheese grater, is a good way to get the worst of both worlds.