Since you are buying factory ammo it is not going to save you anything shooting a .223 except for recoil. Might as well stick to 308 because you can get a factory barrel and start shooting and then get a 6.5 creed when you can make good groups with the 308.
I thought about suggesting the .223 but it really didn't save you anything. If you were reloading you would save on powder, bullets, and brass because it is all so abundant. But buying factory ammo is going to make it irrelevant.
The fact is that factory ammo in any gun is just not going to yield optimal results. You could buy a $5000 gun and run factory ammo, but it isn't guaranteed to shoot any better. Like running e85 in a formula 1 racer.
I am not going to say I have some great amount of knowledge or skill, but I bought a .223 bolt action pretty much straight factory, first gun, that I started reloading for with my first reloads. It took some time fiddling with reloads and other accuracy enhancing projects like bedding the stock, but I shot my first 1/2 moa groups with a center fire.
I think you might be over estimating the time it takes to make decent reloads. I spent about $300 plus dies and I am making accurate enough ammo to shoot a .385 group at 150 yards. I spent some time making different loads, but once that was done it took much less time to crank out some good(enough) rounds. They cost about 25 cent per round to make where you are spending about 1.25 per round to buy. Larger calibers cost more to reload but they are still more accurate than factory and under 50 cent per round. You might be surprised at how much time you might save with hand loads over trying lots of different factory loads.
Bottom line, go with the 308 or 6.5 creedmore if you really only want to buy one gun and one barrel with factory ammo.