wechlish, being new to long range stuff, I recently went through what you are going through now. After some trial and experimentation, and knowing what I know now, I would have gone a completely different route.
I'll just say this to start. I will never again buy an off the rack rifle, unless it's just so dirt cheap that I'd be stupid to say no.
From your post, I'm am going to assume that you have the budget to build a pretty nice rifle. If you decide to go AICS or the like, then more power to you. I would hardly consider an AICS an off the rack rifle. Still, if you haven't had your hands on one, I'd suggest that you get your hands on one before buying. I wanted to buy an AICS chassis and did some research; and apparently there are many that do not like the ergonomics of the rig. The biggest complaints being that the cheek piece did not go low enough and that they were too heavy.
If I had it to do over again and was going to build a semi custom rifle, this is what I'd do.
First, start with the action. I like the 700 action. It's strong, simple and has very few parts. Well, fewer than the Savage with the floating bolt head, anyway. 700 actions can be had pretty cheaply, by either just buying the action for around $400 or buying an ADL model for under $400 and stripping it for the action.
Second, I'd get a a barrel from Krieger (or Rock Creek or Bartlein, etc). $300 or so.
Third, get a trigger. I personally like the Shilen, but have a Timney as well. Each goes for around $125.
Fourth, get a stock. Plently nice stocks out there. Good bang for the buck stocks at $200 to $300 are the HS Precision and the Bell & Carlson line. Both have full length aluminum bedding blocks. If you want to spend the money, there are AICS, Manners and McMillan for stocks starting at around $500 up to the sky.
Fifth, figure out your magazine configuration. This will run you anywhere from about $75 for a "stock" internal mag config to about $700 or so for something that is compatible with AICS mags, including a couple of mags. I'm running Wyatt's mag systems right now. They were cheap and a drop in. I plan to go to Badger when I can afford to be without my rifles for a while. Probably when I go on vacation.
I'm suggesting this route for a few reasons. The first is that you're going to spend the money anyway. Might as well do it right the first time. The second is that the custom barrels will have benefits. You'll get higher velocities due to tighter chamber tolerances. You won't have to load ultra long to get to the lands. The bores will foul much less than just about any off the rack rifle. They will generally be more accurate to some degree.
I'm not saying that taking this route will get you what might be considered a top grade build, but it will be a top notch shooter. The only thing you might change to make it a top grade rifle would be the action, but now that would take you into a whole new ball game with custom actions starting at around $900 for the action only.
I'm running two .308s right now. Both are based on Remington 700 actions. Both are sporting Krieger barrels. One is a 22" and the other a 26" and both are MTU profile barrels. I'm running a Shilen trigger in the 26 that sits in an HS Precision stock. The 22 has a Timney trigger and rides in a Bell & Carlson M40 stock. When I say that they are both tack drivers, I mean that in the literal sense. I have literally shot flies, tacks, nails, paint balls, etc. using these barrels at 100 yards with 168 and 175gr bullets.
Each rifle cost me around $1500 each, plus the glass, my preference being the Nightforce 5.5-22X50 which adds around another $1800 to each. Going this route may not garner a bunch of ooohs and aahs at the range, but they certainly shoot well and won't break the bank.
Just to give you an idea, this is my 22" rig when it was sitting in an HSP stock. I have since gone to a Bell and Carlson M40 because I like the skinnier palm swell for prone shooting, which is what I do with this rifle.