You'll learn early on that there is no 'best' when it comes to components. If there were, we would all be shooting identical rounds!
Each component has its strengths and weaknesses. For instance, a rule of thumb is to use CCI primers in auto loader because they have a harder shell. This prevents slam fires (safety concern). In bolt actions, Federal is arguably the most sensative and is used by many competitors.
When it comes to bullets, each company makes good ones, and not so good ones. For instance, when I load .308 win, I chose to duplicate a military round and used the same one used in vietnam; the 168 HPBT Sierra MK.
I have also heard that Hornady's .224 (.223 rem) FMJ-BT is almost match quality compared to other companies, thus I have bought 100 to test them out.
When it comes to brass; leaving out the match brass like laupa (which usually costs quite a bit more), I find Winchester to be the best, followed closely by Remington, with Federal bringing up the tail end. This is my own opinion after months of testing, thus your milage may very.
This doesn't even touch on the fact two identical rifles may prefer bullets made by different companies, as well as entirely different weights.
The beauty about handloading is that you get to pick and choose the components based on what YOU want the round to do. Bear in mind though, that while each component may not be the best for one thing, may very well be the best for another.