Very solid advise from CT here. More people should spend a good amount of time building a solid base (that is build technique and strength) in the basic lifts before starting with specialisation. When your foundation is rock-solid you will not only be able to progress much MUCH faster going forward, but you will have a solid base from which you can jump to whatever comes next (be it bodybuilding, powerlifting, olympic lifting, cross-fit, or even other non-weight type sports). If you have good technique and build strength on that, you are going to be better off.
I see a lot of intermediate lifters who never did spend the proper time learning and often neglect it going forward. Subsequently they never progress much, get stuck or worse - always battling injuries, and often can’t really (successfully) take on new athletic endeavours. I think those types of lifters would benefit a lot from going back and spending time re-learning the lifts.
As to which accessory work that have best carry-over the answer is: It depends.
It depends where your weakness in the lifts are (and they change over time). In the beginning the weakness is likely overall technique and strength, maybe lack of mobility. Later, when technique is solid, you can start to analyse weak-links more easily and add work accordingly. It is hard to know, without seeing you lift. Most often people neglect the basics which would solve their weaknesses naturally anyway. (Proper bracing and breathing, making sure the right muscles are firing etc.).
So don’t put the cart in front of the horse. That said, you could probably add some lighter BB style work here and there that wouldn’t require much in regards to technique or recovery demands.