Samson
Depends on what you are going to do with it? In my opinion big difference in the route you take. If you are not trying to shoot competition (either 1k BR or some other form) with it, then you can go with about any caliber, action etc and build it for $700 like Jerry said and have lots of fun and learn a lot.
However, If you want to shoot 1k BR now, then pick up a good used gun at one of the shoots. Cost will be $1000-1400 depending on action and number of rounds. New will cost $2000 plus if you build it. Many times they will come with dies and load development already done. Good used 20x or 6-24x scope will cost$250-400 max and serve you quite niclely. You will find that you are going to spend another $300-600 in specialty loading tools and equip depending on how serious you get.
Try to stay with a non-fireform caliber (6.5-284, 300 win mag, 300 Wsm, 300 weatherby etc) and just shoot it for a year. It will cost $300 for new comp 28-30" barrel and $150-175 for installation later, in any caliber that the bolt face will handle.
Same thing for just LR paper/metal shooting guns, you can find a lot of good used guns for sale at half the cost to build. Go that route until you have the experience to know what and exactly how you want it set up.
Finally, pick your gunsmiths very carefully. Sid is a great BR smith for sure. Make sure the smith you are using has experience building the type of gun you want for comp or whatever. There are too many subtle differences in gun setups between disciplines, ability to track bags, throats, chamber specs etc. Those differences make the difference many times in how the gun performs in order for you to get to that top level. Too many general or one specialty gunsmiths think it is easy to build a gun in another discipline that is a winner when they have zero experience buiding winners. Look for the gunsmiths name in the equipment list or winners circle. If not there, probably a reason why no one is using them for that discipline. Remember any gunsmith can build a gun that will run in the middle or lower half of the pack if that is all you want, but only a specialty smith will build the gun that runs in the top 10-25% consistently.
BH