no need for a ducted fan then, which would look unsightly (they are rather big)
If you have not made the hole yet, a 125mm or 150mm will enable you to fit a larger fan, which can be quieter and more powerful than the typical 100mm.
Unless it is directly above a bath or shower and within 2250mm of the floor, you do not need an extra-low voltage fan. If it is liable to be splashed or squirted, you will need a water-resistant fan, which is more expensive.
A cheap builder's fan typically has a throughout of 80 cu.m/hr, which is not enough.
This one is a good maker, three times as powerful, quieter, and has a ball-bearing motor so it runs quietly and will not wear out quickly.
It has an overrun timer, so that, assuming you turn it on when you enter the bathroom and it runs during and after your shower while you brush your teeth and cut your toenails, there will not be much damp, and it will finish off during the adjustable run-on time. It has a backdraught shutter.
It needs a 6-inch hole in the wall, lined with plastic duct. I recommend a cowl vent on the outside to keep the weather out.
I recommend you have it wired to come on with the light switch. Otherwise people will forget to turn it on. It is quiet and cheap to run, so no need to worry about using it.
If you feel the need for increased cost and complexity, and reduced effectiveness and reliability, you can get a humidistat version.