I too would pick the Remington over the Stevens. The Remingtons look better IMO, have less pieces to their bolts, have smaller and trimmer receivers so they are lighter and scopes fit much better with out having to resort to extended bases or rings
The difference between a 308 and 30-06 inside of 300 yards is nothing and you being new to rifle shooting I highly doubt that you are going to be taking shots over 300 yards. Either is perfectly capable of taking anything from coyotes to moose with out a hitch.
If you don't want the 308 and still lean towards the Stevens ask if they have a .270 Winchester. The .270 is, IMO, one of the absolute best deer cartridges ever thought up and just like the .308 and 30-06 will work from everything from coyotes to moose.