RE: Elk Gun?
#1 You should really try to save up a little more money. Even on the cheaper rifles $250 is pushing it. I suggest looking at the Stevens 200. It is the same rifle that Savage sold as the model 110 before they updated it. Not pretty but reliable, functional, and generally very accurate. In order to get a good and reliable gun and scope package you will need to spend about $450 - $500. I do not consider the scopes that companies put with their package deals a reliable scope.
#2. The 30-06 or .270 will be the cheapest two cartridges to shoot and ammunition is available any where ammunition is sold. The 30-06 will have the advantage on elk because of the heavier bullets available for it but both are very effective elk cartridges. You DO NOT need a magnum of any kind to hunt and cleanly kill elk.
#3. The new Mossberg is by no means the same rifle that the old Mossberg was. The old one was a Howa 1500 built by Howa for Mossberg. The new Mossberg is just above the Remington 710 in regards to its build quality. No offence to any that have one of these rifles. They do what they are suppose to do, which is send bullets down range, but they leave much to be desired when it comes to a quility built rifle.
Eagle 338, having the safety lock the bolt closed while on safe is not a really desirable feature to have on a rifle as it forces you to take the gun off safe in order to unload it. It is much much safer if the safety is engaged while unloading. The best safety is a three position as it allows you to lock the bolt closed while walking around in the woods but still be able to unload the gun with the safety engaged. Having the safety lock the bolt closed when it is engages is the least desirable safety feature you could have. At least as far as being safe is concerned.