A secure top is the most important accessory you will buy, because green anoles are quick and persistent escape artists. A locking front door or a screen top with positive latches keeps the animal contained, and it is worth confirming the closure is solid before the anole ever moves in.
Mesh size matters more than it first appears. A top with gaps wide enough to lose feeder insects through—flightless fruit flies especially—undermines both containment and feeding. Match the mesh to the smallest prey you intend to offer.
If your enclosure relies on a removable screen top, add clips or weights so it cannot be nudged loose. A lid that merely rests in place is an escape waiting to happen, particularly in a household with curious pets or children.