I noticed working as a mechanic, that alot of clamps were clamped too far.
This way, they would not go all the way down on the post and would seem loose setting up on the top of the tapered battery lug.
I fixed that issue on many, many people's cars when I would do other work just to prevent a needless comeback.
Make sure the lug is stretched as far as it can be without damaging it.
Then make sure it goes ALL the way down onto the tapered post (unless the post has a ridge at the bottom, this means contacting the plastic case).
Then while holding it down, tighten the clamp part. If you dont spread the lug open, it doesn't matter how much you beat on it or tighten it, it just wont go on good.
I generally only use acdelco, motorcraft or mopar batteries. Acdelco being a favorite.
If you get a cheap battery, I bet the terminals might be undersized. Lead has a cost. Theres a reason that battery was cheaper.
As simple as it seems, as many improper battery installations as I have seen, I would guess most people that install a battery have absolutely no business doing it.