Congratulations on your new property!
I have a few questions. Are you saying that the perimeter fence would be the only fence between the chickens and potential predators? If so a 6-inch opening is plenty big enough to let in weasels and possums, and pretty easy for a raccoon to climb, and 47 inches is probably not high enough to keep out foxes and coyotes, either. Of course if you have a predator-proof coop in which they are locked at night that'll help, but, in my situation I've had four attacks and they all happened in broad daylight.
Will the birds have natural shrubs or low-branched trees such as pine trees to hide under when free ranging? If not I'd plant something that grows fast in various places to provide both protection and the all important shade they'll need during this hot summer.
As for the chickens getting over the fence--some will and some won't. In my mixed flock my biggest, heaviest birds easily hop to the top of a 4 ft post, then hop down the other side. Conversely, my lightest little bantam who actually can fly quite a distance when frightened could be trapped inside a little 3 foot fence all day and never think to fly/hop over it. So, all that to say that it depends on the personality of the bird. Clipping wings had no effect, in my experience, as the birds are hopping...not flying.
I hear you that budgets are always a factor. You might consider a higher chain link fence as that would have smaller holes that'd keep out more things. Or, you might consider a smaller run area with the traditional hardware cloth fencing which truly is predator proof if installed correctly (buried to prevent diggers, etc.). Or, you could free range the birds during the day, with a strong coop for nighttime and natural growth they can get under during the day.
You might contact your local ag extension office to see what the main predators are for your area and what other poultry owners do.
