One item nobody's mentioned (I don't think...) - primers.
I personally use any brass I find, until it dies; once-fired, many-fired... all the same to me. But the first check I make on pistol brass (not easy to make on rifle brass, with old eyes like mine), is look down the mouth of the cartridge and count the flash-holes in the base, leading out of the primer pocket:
1) one bigger hole in dead-centre? - Boxer primed; good cartridge, pocket it.
2) two (or more; occasionally I've seen three) around the dead-centre? - Berdan primed; not nearly as good, and myself, I bin all of those.
The big difference for North American reloaders is that we use Boxer, the Europeans use Berdan. Without going into the weeds, Boxer are dirt-simple to remove the old primer - a decapping pin in the centre of the resizing die goes down that centre hole and pushes it out. Berdan primers are not nearly as easy to remove - the Europeans have a wicked claw tool that 'sometimes' takes it out cleanly, or you can fill the case with water, fit a close-fitting rod down the neck, position the case over a block with a hole drilled in it and give the rod a whack with a hammer, popping the primer out hydraulically - but Berdan primers are not particularly available in North America, and they have a couple different sizes to Boxers - you can't just drill a hole in the centre of the primer pocket and shove a Boxer primer in.
The BIG problem with Berdan primers is that there is no hole in the centre of the primer pocket - so if a Berdan-primed empty finds its way into a run of Boxer-primed empties, and you shove it in your press and haul down on the lever, the decapping pin has nowhere to go and will likely snap-off - and your reloading session just ended (says the voice of experience; .303 was what I started-out reloading, too).
Edit - and North American presses and priming tools are set for Boxer primer sizes, so you'd have to round-up a European primer tool to fit the Berdans; I know neither of my Progressives could handle Berdans, which would greatly slow-down and complicate a pistol reloading session.
So I recommend you make your choice and stick with one fashion of primer or the other - the decapping pin you save might be your own. This can provide angst, if you're picking-up range brass. I wandered down into our indoor range and eyeballed the brass bucket - and lo and behold, there were ~a hundred chromed .45 empties in it! What a sight! - I went head, shoulders and both hands into the brass bucket and started scooping empties - and had most of 'em in my pocket when I started wondering why my fellow club members, brass-hounds all, had not picked them up. So a quick look down the mouth of one - they were Berdan primed.
I left them in the brass bucket, and cried all the way home.
