Hi. 500 yards is too far for a .243. It's a 300 yard cartridge. Even with heavy bullets.
If you're going to change the stock you might as well glass bed it at the same time. You can do it yourself with an Acraglas Kit. About $30 in most gun shops. Follow the directions on the box and bed the receiver and along the barrel channel under the chamber only. This'll give you a free floating barrel. If the rifle doesn't shoot well floated, put a wee pressure point(use a dab of bedding material) in an inch or so aft of the end of the forestock. Rem 700's tend to like a floated barrel, but that's not chiseled in stone.
I wouldn't bother changing the barrel though. Good aftermarket barrels are expensive and the factory barrels are fine.
The Rem 700 has an adjustable trigger so a trigger job isn't as necessary. Go here for a how-to. Keep it around 3 or 4 pounds for hunting.
http://www.quarterbore.com/library/articles/rem700trigger.html
The rifling twist rate is the number of complete turns the rifling makes over a given distance. Your rifle has a 1 in 9 1/8". That means it makes one complete turn in that length. It also means your rifle will likely prefer heavy bullets(80 grains and up.). Most commercial hunting rifles do. Even factory varmint barrels. Mind you, that doesn't mean it won't shoot lighter bullets well too.
Personally, I like the results heavy bullets give on ground hogs. A Speer 105 grain SP practically turns one inside out. A 90 grain FMJ(not the same as a milsurp bullet. They're made for hide hunting coyotes, etc.) makes a puncture wound with no exit hole.
Thanks to the bench rest crowd, there are good match grade bullets available too. No hunting anything but varmints with them though.
