4x is fine for shooting groups at 300yds.
i've shot 1 MOA 5 shot groups at 300 yds with a millet DMS1 (1-4x).
you just need the proper sized target for the range you're shooting. it is very possible to shoot MOA groups at 300 yds with open sights. you'd just need a 36-48" diameter target, and good sights.
4x is good enough to center on the head of a life sized silluette target at 300 yds.
if you want to shoot pop cans, prairie dogs, or golf balls at 300 yds, more magnification would make aquiring target easier.
sounds like you have benchrest type shooting in mind here. if this is the desired role, then get a higher magnification optic.
you should be able to get a pretty good scope for $300. medium end leupolds, nikons, burris, bushnell are in that range. if you're gonna be shooting 3-600 yards, i'd recommend a good scope not only for better optical quality, but also for accurate, repeatable adjustments.
still need a decent mount too, another $80-200.
like the other guy said, "shooting is expensive". especially formidable calibers at longer ranges.
get as nice of a scope as you can, and you'll be be better off. nothing worse than trying to save a little money, and getting a piece of junk. i speak from experience.....should have took the family to dinner instead.