There is no magic time limit. Keeping him indoors (taking advantage of the move as a big change anyhow in his life) will be much better for him all around as he won't be in danger of other animals, cars, all kinds of unpredictable things and people out there. He may be a nuisance til he gets used to the idea, but he'll be alive. Get a harness (the kind that not only goes around the neck but also behind the front legs) and gradually get him used to wearing it at home for short times, then add a leash and take him out for walks (though he may spend more time sniffing one bush and bore you silly).
Why do you have to start letting him outside? Cats do just fine indoors and a lot safer and healthier too. Plus if you let them out, you have to keep up on shots every year because the risk is higher for them to catch things. Indoors you don't have to really worry about shots all the time.