The 270 Winchester is a necked down 30.06 to the .277 caliber. It can drive a very good bullet of 140gr at over 2900 ft/s and a awesome bullet of 150gr to 2850 ft/s allowing it to shoot falter than the .308 Win. and .30.06 with the equivalent ballistic coefficient bullets and less recoil.
This benefit is also the downside since you will find a more restricted bullet selection than the .308 for all type of uses and bullets with even much better ballistics coefficients in the .308 if you know how to manage the higher parabola with your scope and ballistics charts.
On average the .308 is more affordable as the .308 Winchester and 30.06 are both military cases and have been widely spread all over the world. The .308 win is virtually the same as 7.62 NATO military loadings that you can find at retail sales and discount and surplus sales. Also brand new .308 win PMC/Lake city/Priv $10-$11/case that provides great brass to reload.
I cannot think of many things the .270 win will not do but the same is true for the .308 win or 30.06 with even more possibilities in the end of the day. If you are going to do mostly long range then consider the 30.06 as it provides a tad more powder and energy and the .270 flatter shooting and a tad less energy but in either case you have to consider more expense up front in your system, scope, gear, training, etc...
The 30.06 popularity makes it more affordable than the .270 to adquire factory ammo but any when compared to the .308 winchester the .308 win does a lot of things very well and it is the cheapest to shoot of all of them.
In any case at very long range to be able to kill that type of game you need to start considering the magnum and super magnums cases and then the bill goes up quickly,
not just the bullets, but cases, powder, gear, etc...
I personally and for my first system I would stay away from magnum or exotic cases and stick to the .30.06 or the .308 winchester. Those are the every day bread and butter and in .308 win you can find great deals of surplus that you can use to train and get better at it and save the expensive loads for hunting.
Even if you need a tad more speed Hornady just relased the powders for their superperformance ammunition that can give you 100-200 extra fps w/o increasing pressure.
With the 30.06 you will be using 68gr vs. 56gr case capacity for a tad more energy when in reality in most real life situations you will not use it but it is something to consider.
.308 caliber has one of the best if not the best bullet selection out there for almost anything you can think of. Consider a 1:11 rate of twist or even 1:10 for the best bullets and uses although this is not necessary for average hunting.
Regarding the 7.62x39 is not an option at this point so we are passed that if you want accuracy and good bullets. The bullets are .310 diameter and selection is close to none.
A 14year old can shoot a .308 winchester magnum and even a 50 caliber with the proper setup, muzzle brake and training but does it really make sense?
Do we really need a Chevy Corvette to go to the office or supermarket? for versatility, easy of use and cost we probably will do much better with a nice Chevy Impala.
I hope this helps and good luck.
Cheers.
E.