It really depends on what type of shooting you will be doing. The savage actions are a great base for any type of shooting from game to varmints to informal benchrest (club matches and such), but if you are going to compete at the highest level you will need a custom to get there.
As far as factory chamberings in the calibers you mentioned, savage is the only one that I know of that makes both. I believe Cooper makes a 6Br, and you can always build a ground up custom and pick the pieces and parts that you like.
The accutrigger, or any factory trigger for that matter, will not match up with a true custom (jewel, shilen, etc...). However, the accutrigger I have is crisp and consistent. You can get aftermarket triggers for the savage from rifle basix, and now sharp shooter supply (check out savageshooters.com) offers on top of the 12oz competition trigger a 2oz trigger that requires timing of your action, but is well worth it.
When you handle a true custom action you will know why they cost what they cost.
Hope this helps,
Mike