First off,Welcome to long range hunter.
I'll chime in here. The following information is simply my opinion.
If you have other guns to hunt with , wait until you can purchase the custom action you want. There are a couple that come to mind. stiller, lawton just to name a few. The other option of'course is to use an old Remington action.I would go this way if I could fine a cheap donor gun but at the prices that are normal for Remington's I would just buy one of the customs.( This of'course would depend on the price. I have stumbled across a yard sale/auction or two and picked them up for about 250.00-300.00 although it has been a few years sense I have found one.)
You have shown some interest in 338 type rounds so again I would say lawton, stiller something of this nature simply because they are stronger. The gunsmith bill should be cheaper due to less work required.
Now, if you use one to build another with there are only a couple requirements. What is the size of the base of the cartridge. IE, .473 this is a 30-06 family on a long action. the second, the length of the action short ie 308 long ie,30-06 I don't know off hand about the 338 stuff as I don't own one but a good reloading book like Sierra will have cartridge dimensions as well as many internet sources.
Either way do what you think is best with the knowledge you obtain, and let me tell you there is a lot of good knowledge on this site. just decipher the knowledge from opinion not a problem because most here try to just enter what they know. unless you ask about an opinion.
I look at a custom rifle
, be it long range or not, as something you want and will be happy with. Something you will not have any doubt about and be proud to show to your buddies. You will spend a pretty decent amount of cash so make sure it is what you want and you don't settle for less because of impatience's. "the true reason for an unsuccessful hunter"!
I hope I have been helpful but if not just stick around and someone will be.