Cheap and easy way, without a holesaw

It’s easy to make a round cutout without a jigsaw. You can make a simple jig – an oblong piece of wood or metal, which pivots around a bolt in the centre of the circle you intend to cut. A guide-hole in the other end of the jig tells you where to drill your holes – and you simply rotate the jig around its pivot, drilling holes until you end up with a perfectly circular pattern. You can then cut the circle using a coping saw to join the drill holes up.