Kirby's price is right with the components he mentioned but, his price was just under your $3000 budget and never mentioned anything about scope bases, rings and a scope which can easily tack on another $1000 plus. I've figured out some prices keeping your $3000 budget in mind. I have several long range specific rifles and all of them are single shots. There really is no need for a magazine when doing this type of shooting as each shot is meticuously calculated and preppared for. It's simple to just reach into the ammo box and grab one shell, close the bolt and your ready to go. We hit everything on the first shot anyway right?
Here is my prices for a complete custom long range rifle including optics
Stiller Predator Action = $825
Barrel from any top name company = $325
Chamber of your choice = $185
Vais Muzzle brake installed = $150
McMillan stock = $500
Pillar Bedded = $150
Rifle Basix Trigger = $125
Leupold Bases = $25
Burris Signature Rings = $50
Sightron SII 6.5-20 x 50 = $600
Triger Guard = $40
Total for everything $2975
Now you can save money by opting out of some things and upgrading others.
If you already own a Remington 700 action have it single point blueprinted for $150 and use the action. You can still have a Sightron 6.5-20 X but with a 42mm objective and a A/O for $375. This cuts down the cost considerably. Now you can have a complete rifle with optics for around $2100. Now you can upgrade to a Jewel trigger and/or upgrade your optics. That's the nice thing about a custom rifle build. You can pick and choose your rifle options to fit your budget and still have exactly what you want when it's finished. When you have taken in all the information everyone has given you, e-mail or call me at Montour County Rifles
and I'll work up some prices on exactly what you want.
As for cartridge, I'm assuming you'll be hand loading so, as long as you limit your shots to 1000 yards and under the 7mm STW will work just fine along with several other 7mm Magnum cartridges. The little bit bigger .30 cal Magnums will hit with a little more authority though and some can be stretched a tiny bit further, but limit your distance to what you feel comfortable shooting with your experience. Again this is something you can discuss with the smith, as there are alot of good choices.
Good luck with your project.