I think the first step is to determine your budget and work from there. There are some options with off the shelf rifles, there are more options with semi-custom rifles, and lots of options with full blown custom rigs. If you think recoil will be an issue, there are cartridges with less recoil that perform better at long range than the .308. But whatever chambering you choose, pick a cartridge that you can comfortably lay behind for 10 or 20 rounds.
You don't need to spend good money on things that don't matter. I would put a muzzle brake close to the top of the "Don't Matter" list, closely followed by anything that is prefixed with the word tactical. These are generally things that tend to be expensive, make the rifle heavier and bulkier, but do not aid in its shootability. Having said that, you do need to have a concept in mind when you begin a custom rifle project, and the early version of the US Marine Corps M-40 isn't the worst example to follow. They started with a M-700V bolt gun, bedded to a non adjustable fiberglass stock, topped with a fixed 10X scope, and equipped with a good quality leather shooting sling. The result was a rifle that could be comfortably carried in the field, yet was accurate enough to take out threats at very long range.
Rifle barrels are available in stainless and in chrome-moly steels. Both of these steels can be finished with a tough bake on finish that provides excellent protection to the gun, and are available in a wide range of colors to match your personal tastes. Going the custom barrel route will result in a more accurate rifle, but you must decide if you can make use of the difference for the additional $600 cost.
In all honesty, I began long range shooting with a M-17 Enfield .30/06 hunting rifle with a 3-9X40 scope in Weaver rings, so spending $10K on your first long range rifle isn't necessary. Providing you have a rifle and ammunition combination that proves to be MOA capable at long range you're in the game. Becoming a competent handloader is necessary though, because you need affordable good quality ammo. You can't hit at long range with poor ammo except by accident. Ammo thats OK at 100 yards might not even be in the game once you go past 500. A few boxes of Lapua factory ammo will give you some excellent brass to start you off, and will provide an accuracy benchmark to compare your handloads to.
The .308 is not the most expensive round in the world to load for, but with respect to ammunition cost, consider that the bullet is the most expensive component you will have to purchase on a continual basis. There can be a difference of $20 or more between the cost of a box of .308 match bullets and a box of 6mm match bullets of the same brand within normal bullet weights. If you chose a .223, the difference would be more like $30. If you are an enthusiastic shooter that could effect your annual cost by hundreds of dollars, without the higher cost being advantageous to your score.
There are advantages to the large tube variable power scope, but these scopes tend to be expensive. Fixed power scopes with 1" tubes are lighter, tougher and cheaper than variables but you may find that you need a 20 minute base to get enough vertical adjustment. If you choose a fixed power scope I'd consider a 10X or 12X. Mirage can be a problem with very high magnification, and a fixed power scope can't dial below it like a variable. Your scope should have target style turrets for easy adjustment for range and wind. It should also have parallax adjustment, although a focus ring on the objective is just as good, and in some cases better than a turret. Choosing a used scope is one place where a significant saving can be realized.
I believe that the stock is one place where you shouldn't skimp. The best stock you can afford, properly bedded to the action, is the stock you need. If you can afford the luxuries of an adjustable stock, thats fine, but primarily you need to be concerned about the quality of the stock, and its suitability to meet your needs.
Bi-pods aren't for everyone. They add another dimension to the shooting problem that does not occur when shooting off a rest or sandbags. Because you are confining your shooting to the range, I wouldn't put a bipod on your initial list.
Keep good records, both in the loading room and at the range. These records should include the date, location, light, and weather conditions, your load data and your score. The commercially available record books are quite useful, but just a plain notebook works if you remember to include all the pertinent data.