I have built several customs now, from just adding a few bolt on parts myself to full blown, custom work requiring gunsmiths and more knowledge/skill then I possess. I am not the expert here, but I feel I have enough experience to at least offer a few insights that might help you get what you want. I did my first custom build with a similar idea that you have, a target rifle that can hunt. Is it possible? Yes, but there will be compromises that will negatively affect the rifles performance or enjoyment when it is pressed into a role that it is not ideally suited to, plus you said that budget is not a major concern, you can wait to save to get the "right" rifle. I think you are better building a dedicated rifle for the intended primary purpose, in this case a target rifle because you have your hunting rifle needs covered, it seems.
Easiest way is to start with a factory rifle that you like and build from there. Tikka, Remington, Howa, Bergara, and many others make a great place to start. Add a new chassis, upgrade the trigger, put on great optics and you are off and running. Next level is to replace the barrel, we used to do this to get a better barrel than the factory offered, but so many factory barrels these days are great shooters, I have personally had several Tikka plain old factory rifles shoot many sub half MOA groups it makes me wonder why we build full out customs anymore. The main reason to swap barrels is to get something that you can't get from the factory, currently my favourite LR rifle is a Tikka with a Benchmark barrel chambered in 6XC. You will never find that chambering in any factory rifle.
For triggers, I only have experience with Timmy and Trigger Tech, both are excellent, but Trigger Tech is Canadian and I find a little better priced so lately I have favoured them, other than for Tikka because the last I checked they don't have a trigger for the Finnish rifle yet. Chassis and stocks are every where now, from $500 to thousands of dollars. I have used AI, Cadex, MDT, Rhelm, McMillan, Bell and Carlson, Boyd's, HS Precision, and a few others I am sure I am forgetting. Currently I own McMillan and MDT with another MDT on order.
Good luck with your build, any questions ask away, lots of knowledgeable people that love to share their experiences!
Easiest way is to start with a factory rifle that you like and build from there. Tikka, Remington, Howa, Bergara, and many others make a great place to start. Add a new chassis, upgrade the trigger, put on great optics and you are off and running. Next level is to replace the barrel, we used to do this to get a better barrel than the factory offered, but so many factory barrels these days are great shooters, I have personally had several Tikka plain old factory rifles shoot many sub half MOA groups it makes me wonder why we build full out customs anymore. The main reason to swap barrels is to get something that you can't get from the factory, currently my favourite LR rifle is a Tikka with a Benchmark barrel chambered in 6XC. You will never find that chambering in any factory rifle.
For triggers, I only have experience with Timmy and Trigger Tech, both are excellent, but Trigger Tech is Canadian and I find a little better priced so lately I have favoured them, other than for Tikka because the last I checked they don't have a trigger for the Finnish rifle yet. Chassis and stocks are every where now, from $500 to thousands of dollars. I have used AI, Cadex, MDT, Rhelm, McMillan, Bell and Carlson, Boyd's, HS Precision, and a few others I am sure I am forgetting. Currently I own McMillan and MDT with another MDT on order.
Good luck with your build, any questions ask away, lots of knowledgeable people that love to share their experiences!
