Ok.
There are two ways to approach the answer to your question. One way is to buy a relatively inexpensive off the shelf option, shoot long range for awhile, learn a lot, and then build the Rifle of your dreams knowing exactly why you are building what you are building.
The other way is to attempt to bat it out of the park right off the bat, and to build a rifle right from the start that you will learn and grow your skills with that will serve you well even when you develop good long range skills.
I did it the first way, others jump right in, Either method is ok. Unless you are made of money the second method demands that you know more upfront, but given how much info is out there you can definitely succeed that way if you have patience.
Instead of focusing on the cartridge you want first, instead think about it the way you would use a tool. When you go to the toolbox, you don't grab a hammer and then go find something to do with it, you instead go search for a tool that will best accomplish a specific job for you. No tool is good at everything, and they all have advantages and disadvantages, so when you choose you have to prioritize what you really NEED over all your wants, since physics demand none can fulfill every desire. A leatherman multitool is convenient and nice to have around for odd jobs but there are better pliers and screwdrivers and knives out there. You try and skin a buck with a leatherman, though it can be done successfully you'll appreciate why the right tool for the job is critical.
So, you need to be specific. If I don't know you are skinning a buck and you ask for a knife you might get recommended a leatherman tool that has been really convenient...for me that is. Or if you are cutting strings off haybales you don't need an expensive unwieldy 7 inch Bowie.
The 30.06 is known to do many things well but is not the best at anything. If you are thinking about elk, a 300 win mag or 7 mm mag is probably better, but if you are planning on shooting a thousand rounds a year then you will be replacing barrels often-so there are always compromises.
Find a couple good long range, high ballistic coefficient bullets you think will do the job you have in mind, figure out how fast they need to start out to have the energy you need at the max range you will attempt, and that will narrow down the choices for your case. If you go custom, get the best barrel you can find ( I like bartlein or krieger) and find a good smith-don't take the smith decision lightly not many guys are doing truly excellent long range rifles. The most critical part besides a straight barrel is the scope. You will never be more accurate than the scope no matter the rifle.
I started out with a lowly 308 Winchester, on a recommendation from a marine sniper I know I bought an off the shelf, production rifle. It was a Remington 5r milspec. I mounted a Leupold mark4 scope on it, bought a couple cases of Federal Gold Medal Match 175grain Sierra match king ammo, and just went and shot. Got into reloading so I could shoot more for the money, which didn't work because I just shot more period, which in the end is the point. I eventually went the custom route when I wanted more performance and had the skill to make use of it, but even though the long range performance of the 308 is not so good I learned a lot. I still shoot it, and it has dropped a lot of white tail seen though it is fairly heavy. It's wind performance is terrible, but in a way that helped me learn the wind a little better I think. A30.06 would be better, and still has great barrel life so you can shoot it a lot and is fine on elk at reasonable ranges so it may in fact be right for you.
Paying your dues with a rifle like a 308 isn't really necessary with all the excellent long range cartridges out there now but that route really did help me. I like the idea of starting out with something at a medium to lower performance level so you can learn to shoot first. I think you will shoot more that way. If you are really dedicated though you can do the same thing with a much higher performance round, but the expense goes up. Either way, you need to shoot, a lot, and the easier and more convenient and fun that is for you the more you will do it. You need a good rangefinder if you are setting up targets yourself, a good ballistic computer/app, good ammo, and a GOOD scope(don't skimp here, get one better than the rifle if you have to choose where to prioritize). So the start up costs are there but you are going to have a ball.
In the end, having said all that, don't be too hung up on the rifle, as long range is mostly about you anyway. Your focus needs to be on your skill, not matter how good or bad the rifle is. By the time you outshoot most off the shelf rifles, you will be able to answer these questions for yourself.
