168gr HPBT match from Sierra or Hornady will work great in both rifles. Cheap 150gr FMJ for the M14 is just fine, but a waste of powder in a nicer rifle like your Remington since you won't achieve the accuracy it is capable of with bulk FMJ bullets. You will want a powder suitable for the M14 gas system along with bullets in the 147-173gr range so as to get reliable operation and not hurt your operating rod.
It is generally recommended to load between 147-173gr bullets for the M1 Garand or M14 using standard jacketed bullet loads.
A powder in the suitable burn rate range for the action of this type of semi auto gas rifle such as IMR 4895, H4895, AA 2495, BL C2, H335, Win 748, IMR 4064 (and there are others).