Been through this before.......THE best way for me was to buy a K & M neck turner with the PROPER DEGREE CUTTER for the cartridge neck/shoulder degree that you are turning, it is a MUST! Go into the shoulder just a tiny bit and it will take care of your "brass"donut problem.
If you decide on neck reaming, which you do you. I tried it and idk, it works but it's not that easy/efficient. You can go on amazon and get a high speed chucking reamer for cheap, put it in a drill and go.
I've seen others say that it won't affect runout but I don't see how it can't, the "brass" donut is at the bottom of the neck and is leaving the top of the neck unsupported making it have runout. I've had more runout with a donut than without.....As others have said, donuts can screw a lot up, es/sd, pressure signs and be detrimental to accuracy at long range. Depending on caliber I'd say anything under 500yrds it's not going to make a tremendous difference....what I found out is the smaller the bullet the more effect it puts on the bullet so I'd say a .224 would probably be around 300yrds and under where it won't make that big of a difference.