If I was going to pick only 3, for the purposes of the hunting I do, which is mostly high country long range deer/elk where you have the possibility of running into grizzly bears, and high desert pronghorn, all of which can REALLY stretch ranges out......
1. Lightweight (9ish lbs) .338 Norma Magnum/.338 RUM:
Fitted with a good brake like a Terminator T3 or MBM Beast 5 port, recoil would be very manageable sending 300 Bergers, 285 Hammers, or possibly the 300 ABLR if it ever comes out, offers excellent wind defying ballistics, plenty of retained energy velocity when really stretching your shots out to 1000 yds or more, and also has the knock down for bear should you have that encounter.
2. Lightweight (7.5 lb) 7mm Remington Magnum:
An excellent option for high country mule deer and elk, especially if your hunting in areas where bear are not as likely to be encountered. With a Berger 180 or similar, you still have a very far effective range and excellent wind ballistics. With a muzzle brake, recoil will be light, and having an overall weight of 7.5 lbs is plenty light to pack really far, and just enough weight to still be relatively consistent at long range.
3. Heavyweight (12-14 lb) 6.5x284, 6.5 PRC or (my preference) .260 AI:
For high plains Pronghorn, this is my preference. The extra weight makes it very shootable for anyone to use and still have little or no change in impact, and with the addition of a brake there is no recoil. Many people use my rifles, so this is important. Using the high bc bullets like the 156 Berger, wind drift is minimal, and effective range is very far.
The 9 lb .338 NM can do all of it, though recoil may be a small issue for younger kids, being that it is about like a sporter weight .308 win. Other than that, I feel like this is a great do it all rifle. Also the reason I'm currently building one.