LC is good quality brass and would be a good choice for 99 percent of most shooting needs. It is the brass used by all US military forces, thus it is readily available and relatively inexpensive.
Lapua is premium brass and would only be advantageous when you are tying to squeeze the last little bit of accuracy out of your ammo.
I use CCI 400 primers and have never had a problem with them.
I have a Dillon carbide 223 sizing die and it’s a good die, but it doesn’t make ammo any better than my Redding or RCBS dies, it just cost more.
For straight wall handgun, carbide dies are almost a necessity but because the brass still needs to be lubed for bottle necked rifle, they are not.