Go get training. The human is always the weakest link in accuracy. It's not arguable. It's a solid fact. Honestly, if one has good fundamentals, they don't need a special trigger unless your splitting hairs. 1/8 moa type hairs.
If you are talking strictly mechanical? Scope. Get a quality scope. It's not a optical device at its primary function, it's a telescopic sight. If you're sight is cheap and finicky, so will your shooting be.
Are you talking specifically mechanical on the rifle? The stock. The reason I suggest that over say, blue printing, or barrels is because a good stock, or even a modular stock compliments fundamentals of marksmanship….the most important thing of accuracy, right? Having the right length of pull, and the right comb height, or more simply a proper setup is critical for the shooter to be consistent.
Blue prints give small gains, and barrels now a days even from the factory are good enough in most instances. My wife took at cheap ruger American off the shelf and shoots 1/4 moa with it for example with no modification other than a cheek riser.
If you're fundementals are solid, you have a decent scope and a rifle set up for you're body…you're good to go. If you get to a point you want to be more competitive, or further your accuracy, then barrels, and blue prints, even triggers and other gizmos can help with that, but they aren't required.