Yes, you swap the entire trigger assembly out. It's a drop-in unit held in with 2 pins. You might be best to have a professional do it. As for the stock, factory Remington stocks suck...Most factory stocks for all rifles are cheaply made and are not very rigid and stiff. If a stock has flex in it, it's not going to fully hold the recoil lug and action in the same exact place every time, it will flex when the rifle recoils as the shot is fired, and can cause accuracy issues. This is why upper-end rifles that have factory HS Precision and McMillan stocks on them, are typically worth the higher price, because otherwise, you will be upgrading your stock as time goes on, which is going to end up costing you the same amount of money as just buying the higher priced factory rifle with the good stock to begin with.
Granted, I know most folks don't always have the cash to drop on a higher priced rifle...I've been there. So, slowly doing some upgrades like buying a better aftermarket stock, an aftermarket trigger, and having the action bedded and the barrel free-floated can make drastic improvements in the accuracy of a factory barreled action.