You can spend as much as you want on something like this and it's easy to let the price get out of hand. My rifle is built on a used CheyTac model 310 action and Chassis that I picked up for $1500 for the set over on Long Range Hunting. These are the same as a Lawton Model 8000 and a McRee chassis made for CheyTac. The barrel is a 30" Bartlein 1-9.5" twist 1.3500" for 5" then taper to 1" at the muzzle that I picked up on sale (in stock right off the shelf) from Bullets.com on sale for about $350. The muzzle brake is a Terminator T4 that was $240; I love this brake but there are lots of really effective brakes that are less expensive. The trigger is a Jewell JT-09 and was about $200. Throw a couple hundred bucks on top to cover the gunsmithing fees and that's it.
If I were you, I'd decide how quickly you want to put the rifle together. I you're not in any rush, shop around and look for a good deal to pop up on a Stiller Tac 408 action. I've seen new ones go for under $1000. Same goes for stock if you're not too picky. I sold a spare McRee Big Bore repeater chassis for $400 a while back. Watch for somebody selling a quality 338 blank and you can save money and time. With a lot of guys moving over to the 375s these days you can find some good deals on 338 blanks.
Unless you plan to build a couple of rifles in this chambering don't bother buying a reamer. Between a rougher/resize reamer, finish reamer and headspace gauge you'll be into it $400+ just for reamers. You can rent a 338 SnipeTac reamer or hit me up when you're ready and I'll rent you my reamers. All the different variations of this case will perform pretty much the same so just pick whichever one is available and go with it. I found my reamers used for a good price and I planned on having a couple barrels cut so it made sense to just buy them.
Or, scrap the budget and just go all out! That's what I did when I built my matching SP! Nothing will run up the price of a build as fast as nice wood, a Bat action and a top name smith to "throw" it all together.
