I am not a huge fan of the 308 as a caliber, personally preferring BIGGER calibers, but from what you are planning to use the rifle for, I think the 308 would be your best choice of the calibers you list. Personally I think there are better options in caliber than what you have listed.
Both magnums will have more recoil than the 308, even with a brake, you will find it taxing to put out the near 100 rnds in a day that some competitions shoot. Many competitions do not allow brakes, so that is another consideration.
Barrel life will be double with the 308 what either of the magnums is.
Cost of shooting the magnums will be slightly higher due to powder volume, this is not a big deal, but it all adds up. Precision brass for the magnums is significantly higher in cost compared to the 308.
You can easily kill deer out to 500 yards with the 308 so no need for the magnums at that range.
Not all competitions and ranges are magnum friendly.
If your intent was opposite, with more long range hunting involved the 300 Win Mag would get my vote. I have killed game at 1000 plus yards with a 7Rem Mag, but I believe it is at the very end of its capability to do so at that distance.
The big 30 cal bullets are a far better way to go in that regard, simply because of the greater retained down range energy and velocity, not to mention wind drift is less noticed on a heavy bullet.
I tried a fun type competition last year with my 338LAI and found it was physically exhausting more from the muzzle blast and concussion than the recoil as the brakes I build are extremely effective. For 1500 yards and beyond the 338LAI is hard to beat, but there are no formal competitions that will allow it yet and there are very few ranges that are that long, so this years comp rifle will be a 308, for all the above noted reasons.