Have and use Lee, RCBS, and Dillon products. I load all precision ammo on the Forster press.
What I like about it most, is the repeatability and "feel" I get both in sizing and seating. The design keeps everything in line, and using the short handle gives you an amazing amount of tactile feedback, allowing you to sort, or at least know there are variances in the processes. I can't get that from the other presses.
Recommendations for precision:
Buy full length sizing bushing dies. I use Whidden, but there are a lot of good dies out there. Pick one and stick with that brand, as they are all a bit different in functionality.
Set up your reloading process, and stick to it religiously. It will change over time, but following the same process every time yields repeatability and precision.
Use seating cones that match your bullet's shape/ogive. This will reduce runout, along with neck tension .002"-.0025" for target loads.
If you are concerned about "runout", get a Sinclair (or equal quality) runout gauge. Don't waste your money on the Hornady unit (if you try to straighten out a cartridge, it makes it worse. Ask me how I know..).
Above all, strive for consistency. The more consistent you are, the better the ammo. Eliminate as many variables as you can, which will reveal other factors that affect accuracy and precision.
Then, you can start on environmentals (wind, terrain, etc.), which make a much bigger difference than any part of hand loading.