I have a 338 Lapua Ack Imp and it weighs 22 lbs. It is not a carry gun, it has a brake and with a 300 it will "push" then.
I would suggest you decide how light/heavy a gun you want first. If you are talking carry weight, then you have to use a brake with the 338 and keep the barrel to 26" probably.
You might want to consider a 30/338 shooting a 210-220 gr bullet. That is flat, accurate and will take anything in North america. You could go down to 26" barrel.
If I was building an "ultimate" then I would look at 30" barrel 30/338 Lapua unless you really want the 250-300 bullet. Use a barrel bedding block, and a stock with 3" foreend and plan on shooting off a rest. If you want to shoot off the bipod, then either the McMillan stocks or one of Bruce Baers laminates that will fit one of his bedding blocks.
Now for action, go with Stiller Python in either left bolt and right port or dual port. Cost is $950 with trigger guard and tapered rings. Hard to beat and no barrel block necessary. It is single shot, but large enough to take a 1.25 barrel and not need a block and will easily take the 338 case.
BH