I'd recommend a 30-06 especially since you will be doing factory ammo only.
There are "reduced recoil rounds" available from the factory if you are "recoil tender" yet these same cartridgeswill still be plenty ample for whitetail. Then, later whenyou decide to go after elk you can go with full strength 180 grainers for somevery adequateelk medicene.
Check out this poll of experienced elk hunters from this very site voting for their actual, current, favorite elk cartridges.
http://forum.hunting.net/asppg/tm.asp?m=1142362
The 30-06 (especially for anon-magnum cartridge near the lower end of the "power scale")was certainly well represented and IMHO constitutes a sound choice for an cross over rifle (deer and elk). Again,
especially since you don't handload, the exceptionally wide range and highly available offeringsof 30-06 ammo that are on the market today are outstanding.
This last season, we had a 13 year old lady weighing little over 100 pounds take her first elk using a 30-06. It is truly a versatile cartridge.