I focus on chamber/ barrel, ammo, sights and trigger. For sling shooting such as in highpower - def a FF hand guard.
Having a well cut chamber and quality barrel with matching ammo is extremely important to the accuracy. So many chambers are cut with reamers that are used for mass production. They wear out, get sharpened and produce a range of tolerances and quality.
A good trigger that allows manipulation without moving the gun is also critical - a good 2 stage trigger (Geiselle) is what i prefer for precision shooting.
Precision sights with good repeat ability is also important when changing distances
The only only other recommendation I would make is the use of a bore guide when cleaning so you don't wreck that well cut chamber. proper cleaning methods, tools and solvents go a long way to keeping it accurate.