I usually use whatever I have in adequate quantities from what I've picked up off the ground at various ranges. I do sort by headstamp.
However, I have noticed some trends through the years, and this is what I've seen.
In handgun brass, I've gotten best results with Federal, particularily, .38spl, and 9mm.
Hornady, and some other smaller manuf.'s use Starline brass. Starline is the very best brass I have used for uniformity, and is what I use in 9mm and .38spl match ammo if not using Federal.
Rifle Brass:
Norma has been best, with Lapua close second. (in .22 and 6mmPPC, both needed primer pockets turned, and necks turned to match rifle's chamber). In my .30/06, none has proven equal to some Norma I obtained in 1975, and am still using!
Federal has been best of American brands, with Rem and Win close behind.
Some PMC I had in 7mm-08 would chamber only with difficulty in a Rem M-7. After neckturning however, it is the most accurate brass I have for that rifle.
Some variation can be expected in different lots of brass. For instance, I have some .243wcf brass by Federal, and there are two distinct "groups" of brass, some weigh 161gr +/-2.0gr, and others weight 174gr +/-. Near max loads in the former, are definitely over max in the latter. I mention this because a friend blew the bolt on a m788 in .243 about 10yrs ago. The load was a mid-level load, and had been safe in other brass. The culprit was in a different headstamp that had found its way into his brass collection for that rifle.
Hence, treat all brass as "unknown" until you have checked it out during prep.
Inspect regularily and discard at the first signs of distress.
In some chamberings, only one or two different brands are available. For instance, .300 Rem. UltraMag is only available in Rem in new -NUF; and only other manuf. of new factory ammo is Federal, so; I HAD to go with Remington, or buy Federal at over $40.00/box of 20!!!