For the M1 and 1903a3, some good FMJ's are what I like to use. Hornady is what I have most of. None of my .mil guns are MOA and they all shoot about what I expect them to shoot.
For the hunting rounds, you have a whole lot of choices. I'm particularly fond of the Nosler line myself - the Accubonds, Ballistic Tips and the Combined Technologies rounds are far and away my favorite. I've had nothing but great accuracy when I do my part and performance has never failed me.
That being said - Sierra, Hornady, Winchester, Berger, Barnes and most other major brands all make solid hunting projectiles that will do the job as long as you do yours. Find what works best and stick with it IMO and don't worry about needing the latest and greatest or best marketed round.