I'm very fond of the "Soler & Palau" fans which are of good quality. They all seem to have ball-bearing motors, which are durable, and are much quieter than older or cheaper ones.
I think your fan will have a110mm duct through the wall, so you will have to fit a similar size of fan. They are not very powerful unless you buy a ducted inline fan (which is much bigger and I don't see that you have room)
this would fit Compare the electrical usage and db noise numbers with any others you consider.
As it is quite a small fan, turn the Time Delay to maximum, and use it whenever you go in the bathroom. It is so quiet and economical that you could leave it on permanently if you have a damp problem. 8W means it runs for 5 days and nights on about 15p of electricity.
It will work more effectively if the door and window are shut. It will draw in dry air through the gap under the door. Dry air is heavier than water vapour, which will rise towards the ceiling where the fan will remove it.
If you can bear it, you could fit a larger and more powerful fan. An inline fan can go above the ceiling where it will be out of sight. It can be quieter and much more powerful, if you have access, for example in a loft, and can run the duct out through the eaves or gable wall. Or if you can have a larger hole made in the wall, you can have a larger, more powerful conventional fan.
The S&P fans are sometimes sold under other names. I can't recall a source but will re-post if I do.