Your best results will be with a router. Though I understand the cost is not in everyones budget. Though if you plan on doing a lot of computer/wood.metal work I would highly recommend a DW621 as it can be used to cut aluminum holes as well. I would personally avoid a jigsaw as one slip up and your screwed. The next best is a hole saw. Don't use a harbor freight hole saw if you are looking for a good finish use a 4 1/2 inch(120mm) Irwin or Bosch. Then like mentioned above sand with 180,220,320, 400 sandpaper.
If you decide to go with a hole saw make sure you first drill a pilot hole from 1/8in to 5/32 then to your hole saw drill bit size for the most precise cut with least wobble. Depending on the thickness of your wood will help you decide if you need scrap wood with you.
If it is a thin piece of wood I would recommend putting it in the middle of two other pieces the same size to prevent wood chipping. Also use this method if the wood has been laminated to prevent the laminate from ripping up.
I hope this helps
-steve