Some Ford Chevy concepts here, but here is my two cents. Will start off with some generalizations.
Are you coming into this as a reloader? If so, the 270 is boring as there aren't as many options at the 308 or 30-06. Learn to like 130 grainers seems to be the middle of the road that most settle on.
Distance with a 270 will be more iffy to wind drift than a 30-06 heavier options.
Using a budget gun, the 308 will be easier on the shoulder than the 30-06 so you can shoot more type of loads.
Scopes are unique. If you get a cheap scope that works well, over time with higher recoil, that cheap scope will make you want another cheap scope so get a good one to start with.
When you think about distance, out past the 500 yard stuff gets into more spendy equipment to really nail it down consistently. Other than that you lob and hope for the most part.
Use a chrono for your load development and find the best chrono to accuracy load you can find.
Look into trigger and glass floating and other options before you buy for better accuracy.