I would consider the following; How does the current configuration shoot? The caliber you are using is very capable of taking game at your prescribed distance. I would consider getting the trigger replaced or have the factory trigger worked on by a gunsmith. Depending on the smith you could have it done for as little as $20.
For optics I would consider your price range. In my opinion, Nikon ($300-$800) (Which I have on two rifles) and the Bushnell Elite($350-$800) series would be my pick for inexpensive scopes. Both very good glass for the money. You could go much more expensive using Leupold ($400-$1200) or the Night Force and IOR ($1000-$2500). The more you spend the better the glass is going to be. You should look for something with no less than 10 power, but should consider up to 20-30 power max. Variable powers are the best option. Another thing to consider is your scope base and rings. This can vary from $40 to $300 depending on what you get. You should look into a one piece base and a good set of rings. I use the Burris XTR's.
Barrels are up to the individual buyer. Personally if the factory barrel is in good shape, shoot it until you kill it. Buy then you will know your equipment and ready for a quality barrel. The factory barrel should be capable of .5" to .75" groups at 100yards. You may want to look into having your factory barrel recrowned for accuracy. Have a smith look it over and they will be able to tell you if it is necessary.
Next is its stock. Do you want a better stock or fix up your own. A good glass bedding job should be all you need, but some like to get out of factory stocks and upgrade to a quality after market. The super sniper stock by Choate($150-$200) is probably the best stock for the least amount of money in my opinion. From there you graduate to Bell and Carlson and McMillian($230-$700).
After market triggers are numerous for Remmy's. They can very in style, pull weight and price. Some gunsmiths can get your factory trigger to break as crisp as you want it, but depending on how light you want it, you may have to upgrade. For a factory adjustment you are looking at $20 to $40 for a smith to work over the factory trigger. For a custom after market you are looking at $130 and up.
The action you can leave as is, or you can have it trued and blue printed. To do this it can cost a lot of money. It depends on what you want done with it. Generally the actions from factory are in pretty good shape. I have never had an action trued and can not give a cost estimate.
Last but not least is the ammunition. Are you hand loading or using factory ammo? If you are using factory ammo, you need to use premium stuff. Black Hills and Federal offer some really nice stuff. If you hand load, the cost can very on what powder you choose to use and bullets. Berger bullets are more expensive than Hornady or Sierra, but depending on your rifle, it many like the lesser expensive bullets. You could look into Barnes and Nosler which I find to be more expensive. I usually use Sierra's and Hornady's. I have hade good success with them both. You need to consider your brass options and primers. Norma, Nosler Custom and Lapua are your premium brass, but come with a premium price. Winchester and Remington brass can be just as accurate if you take the time to prep it correctly. I use Norma for my .308 Win., Winchester for my 300 WSM, and Rem. for my .243. I get really good accuracy with all of it.
Well I hope this helps,
Tank