Welcome to LRH. First, why not stick with the 30-06? It is a good long range caliber. As for the PSS barrels, you always take a chance at purchasing factory tubes. Some shoot well, others are being sold for a reason. I would use that $700 and use some to get a good aftermarket barrel. You can buy Factory reproduction barrels from barrel makers at a pretty good price. Look up Sin-Arms.com. He sells some very good barrels for $275. Another option would be a Shilen match barrel or even a blank from midwayusa.com. These are much better alternatives to the factory barrels people are selling. Can't go wrong with a Choate or Bell and Carlson for a budget minded build. There are some very nice stocks for sale at Stockysstocks.com for most Remington models. As far as the trigger, you don't have to purchase a new one. There are some pretty good instructions online how to adjust it your self. If you don't feel confident in doing it your self, then take it to a good gun smith and have him make the adjustments. Remmy triggers can be adjusted very crisp and clean. There are some other sites online that elude me right now that offer some other barrel makers. You can buy Kreiger or Brux on some sights. If your Remmy has a wood or laminate stock, just have pillars put in and have it glass bedded.
As an avid shooter of the .308 Winny, I suggest a 1:12 twist. It will handle most of the factory stuff to include match ammo produced. If you want to shoot heavies, then a 1:10 twist would be the better option. If you want velocity, a 30" max in length would be the ticket. If you want something you can carry and plan to sit some, then a 26" would be the ticket. If you want to do a lot of walking and have easy handling characteristics, then the 24" is the best option. If you can find a barrel with 11.25 twist, then that would be the best do all for the .308. Make sure you get good glass for your rifle.
As you will need a lathe to headspace the new barrel, talk to your gunsmith and see what he suggests.
Tank