for the orig question - the first and most important tool is a good runout gauge. EVERYTHING else is based off your measurements. The tool price is of no relevance unless they work as desired. I have used both cheap and expensive gear that have both succeeded and failed. Check the tool - forget about the price.
For a press, used a bunch and as long as the ram is not bent or goes way off line, it does not matter. I use a Lee challenger Breech lock press to make all my ammo and I do compete at 1000yds.
For me, this is what I focus on:
Annealling - do it properly and do it often. Every 2 to 3 firings as I am just a bit too lasy to do it each time....although it can help
Case neck prep - measure and maintain dimensions. It likely changes with each firing. If using a bushing neck die, be prepared to outside turn EVERY firing. Time for a quality ball micrometer and a good outside neck turning tool.
Better neck sizing die - Lee collet neck die. Tried many for a range of chambers I have shot. No measureable runout and very nice neck tension. Watch the amount of sizing as this will affect runout.
If using bushing neck dies, see neck prep. Check your die as some WILL create runout.
Better seating die - Forster for me. Others love Redding. If runout is low, inline seaters do no better. Check your tools and change what needs to be.
Primers - confirm each lot and type. There are BAD lots out there. Good time to invest in a quality chronie. Confirm with target at distance cause that is the ultimate goal.
Powders - modern extruded powders from a quality brand. Sorry, haven't found a ball type powder to work well.
Weigh every charge - I hold my loads to the same 0.1gr and it shows on target at LR.
Runout - to be honest, I spend little to no time checking my gear after I confirm that my tools work initially. I have tested ammo with some very high runouts and groups didn't show much/ any difference. Test, test, test.
Powder charges matter. Runout, not so much.
But the only way to convince yourself is to do a blind test on the ammo.
Let the target tell you what you need to adjust not your perception on what is important.
YMMV.
Jerry