Just my opinion and others may or may not agree... The biggest thing I would steer clear of is ammo with steel cases. IDK if anyone makes steel cased .308 ammo or not for that matter.. But I know one can get AK rounds with it.
But cheap ammo is cheap for a reason... While your rifle may take a liking to it, don't expect terrific consistency. You get what you pay for.
Better yet, make your own ammo!
But as far as hurting your rifle, I would not have that worry so long as the cases are brass... Something about steel cases just doesn't sit right with me... That is just my personal opinion and may be totally unfounded.
And you are making the right decision getting the 700. The 710 I spoke of above is the predecessor to the 770 you are looking at. From what I gather, the differences between the old 710 and current 770 are mainly cosmetic. And being that I have experience with both the 710 and 700 (albeit a very entry level 700 ADL) I can tell you firsthand that ANY 700 is a hundred times better than ANY 710/770.
Beyond that, I much prefer a Winchester m70 to the 700.
After I got my new SG in 338WM last November, my little ADL never went in the woods again the rest of the season.. Yes, I felt bad... And I'll still hunt with it. But daggum that SG is NICE!