Richard,
You can use any size bit within reason as long as the radius from the centre of your point to the edge of the bit (ie where it will leave the cut edge of the circle) is what you want. However, I would use a quarter inch bit - there is less spruce to cut and therefore a generally easier job.
A straight cutter or a spiral up cut bit would work fine.
For a one-off job, I simply screw a bit of 3mm hardboard to my router base and stick a brad through the hardboard into the workpiece. If I absolutely cannot tolerate a hole in the workpiece, I stick the brad through a bit of thin wood and use doublesided tape to stick that to the workpiece. In that case you have to "crank" the temporary router base, making something that looks a little like frying pan where the router sits on the "pan" and the nail goes through the "handle".
There are similar methods to use bandsaw or even a table saw to cut out circles, I can probably find a reference if you need one.