Make the fill valve nut snug but remember it is plastic don't over do it, it should be tight enough so that you can not move the fill valve with your hand.
If you have a supply tube like the one in the first image at the top of this page, you may want to replace it with a metal flexible toilet supply, Don't use the white or gray plastic ones, again don't over tighten the nuts. when you turn the water back on check for leaks, one hour later, check for leaks again. Remember The smallest leak can cause thousands of dollars of damage to you home. Maybe you should have it done by a pro. This is very important DO NOT push the rubber hose down the overflow tube, even if it has the adaptor with the hole in it that the hose fits perfectly in to. YOU MUST use the clip that comes with the fill valve and hook it on to the overflow tube. the tube is long enough so that you can put a loop in the hose, do not cut the hose.